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NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles -Download PDF

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NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles -Download PDF

Edited By Ramraj Saini | Updated on Feb 07, 2024 05:09 PM IST

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles - Topics like how to identify different lines, line segments, and angles in the shapes are dealt with in NCERT of Class 6. In this chapter, we deal with lines, different kinds of angles and their measurements. The solutions of NCERT maths chapter 5 lines and angles class 7 give an explanation to all these questions. These NCERT Solutions are given here with a step-by-step explanation of each and every problem of NCERT textbook. In this chapter students are always confused between a line, a ray and a line-segment. So, let's discuss each term one by one- A line segment has two endpoints. If we extend these two endpoints in either direction endlessly, we get a line.

In the NCERT solutions for Class 7 Maths chapter 5 lines and angles, we will study questions related to different kinds of angles like complementary angles, adjacent angles, supplementary angles, vertically opposite angles; pairs of lines like intersecting lines, transversal and many more. Here you will get NCERT Solutions for Class 7 . Before going through the solutions, it is advisable that students must refer to the NCER Class 7 Maths Syllabus and know the exam pattern and important topics.

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7- Important Formulae

Complementary angles: ∠A + ∠B = 90°

Supplementary angles: ∠A + ∠B = 180°

Linear pair: ∠1 + ∠2 = 180°

If two parallel lines are intersected by a transversal line then:

  • Pairs of alternate interior or exterior angles are equal
  • Pairs of corresponding angles are equal
  • Interior angles on the same side of the transversal are supplementary

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 - Important Points

Following are some important points discussed in lines and angles class 7.

Complementary angles: Angles ∠A and ∠B are complementary if their measures add up to 90 degrees.

Supplementary angles: Angles ∠A and ∠B are supplementary if their measures add up to 180 degrees.

Adjacent angles: Have a common vertex and a common arm but no common arm on either side of the common arm.

Linear pair: It is a pair of the adjacent angles whose non-common sides are opposite rays and the sum of both angles are 180°.

Vertically opposite angles: When two lines are intersected, vertically opposite angles formed are equal.

If two parallel lines are intersected by a transversal line then,

Pairs of alternate interior or exterior angles are equal.

Pairs of corresponding angles are equal.

Interior angles on the same side of the transversal are supplementary.

Free download NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles PDF for CBSE Exam.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

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NCERT Solutions for Class 7 Maths Chapter 5 Questions and Exercise

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.2.1

1. Can two acute angles be a complement to each other?

Answer: Yes, two acute angles can be complementary to each other.

For e.g. Acute angles 20^{\circ} and 70^{\circ} are complementary angle as their sum is 90^{\circ} .

2. Can two obtuse angles be complement to each other?

Answer:

Since obtuse angles are greater than 90^{\circ} . Thus two obtuse angles cannot be a complement to each other. (as the sum of complementary angles is 90^{\circ} .)

3. Can two right angles be complement to each other?

Answer: The sum of angles in complementary angles is 180^{\circ} . Thus two right angles cannot be complementary to each other.

1.(i) Which pairs of following angles are complementary?

01

Answer: Sum of the angles in the given figure is : =\ 70^{\circ}\ +\ 20^{\circ}\ =\ 90^{\circ}

Thus two angles are complementary to each other.

1.(ii) Which pairs of following angles are complementary?

1643866616640

Answer: The sum of the two angles is : =\ 75^{\circ}\ +\ 25^{\circ}\ =\ 100^{\circ}

In complementary angles sum of the angles is 90^{\circ} . Hence given pair of angles are not complementary.

1. (iii) Which pairs of the following angles are complementary?

1643866657060

Answer: We know that the sum angles of complementary angles is 90^{\circ} .

In the given figure: Sum of angles is =\ 48^{\circ}\ +\ 52^{\circ}\ =\ 100^{\circ}

Hence given pair of angles are not complementary.

1.(iv) Which pairs of following angles are complementary?

1643866693169

Answer: The sum of the two angles is : =\ 35^{\circ}\ +\ 55^{\circ}\ =\ 90^{\circ}

In complementary angles sum of the angles is 90^{\circ} . Hence given pair of angles are complementary to each other.

2 .(i) What is the measure of the complement of each of the following angles?

(i)45^{o}

Answer: We know that the sum of complementary angles is 90^{\circ} .

Thus the complement of the given angle is : \Theta \ =\ 90^{\circ}\ -\ 45^{\circ}\ =\ 45^{\circ}

2.(ii) What is the measure of the complement of each of the following angles?

(ii)65^{o}

Answer: The sum of complementary angles are 90^{\circ} .

Thus the required angle is : =\ 90^{\circ}\ -\ 65^{\circ}\ =\ 25^{\circ}

2.(iii) What is the measure of the complement of each of the following angles?

(iii)41^{o}

Answer: We know that the sum of complementary angles is 90^{\circ} .

Hence the required complement of the given angle is : \Theta \ =\ 90^{\circ}\ -\ 41^{\circ}\ =\ 49^{\circ}

2.(iv) What is the measure of the complement of each of the following angles?

(iv)54^{o}

Answer: We know that the sum of complementary angles is 90^{\circ} .

Hence the complement of the given angle is : \Theta \ =\ 90^{\circ}\ -\ 54^{\circ}\ =\ 36^{\circ}

3. The difference in the measures of two complementary angles is 12^{o} . Find the measures of the angles.

Answer: Let one of the angles be \Theta .

It is given that the angles are complementary to each other. So the other angle will be 90^{\circ}\ -\ \Theta .

Further, it is given that the difference of the angle is 12.

So the equation is : 90^{\circ}\ -\ \Theta\ -\ \Theta\ =\ 12^{\circ}

or 2\Theta\ =\ 90^{\circ}\ -\ 12^{\circ}

or \Theta\ =\ 39^{\circ}

Hence the two angles are 39^{\circ} and 51^{\circ} .

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 Topic 5.2.2

1. Can two obtuse angles be supplementary?

Answer: No, two obtuse angles cannot be supplementary as their the sum of angles will exceed 180^{\circ} .

2. Can two acute angles be supplementary?

Answer: No two acute angles cannot be supplementary.

For being the supplementary angles their sum should be 180^{\circ} .

But the acute angles are less than 90^{\circ} . Hence their maximum doesn't reach 180^{\circ} .

3. Can two right angles be supplementary?

Answer: Yes, two right angles are supplementary as their sum is 180^{\circ} .

1. Find the pairs of supplementary angles in Fig : 1643866724771

Answer: We know that the sum of the supplementary angle is 180^{\circ} .

(i) Sum of the angles is : =\ 110^{\circ}\ +\ 50^{\circ}\ =\ 160^{\circ} . Hence the angles are not supplementary.

(ii) Sum of the angles is : =\ 105^{\circ}\ +\ 65^{\circ}\ =\ 170^{\circ} . Thus the angles are not supplementary.

(iii) Sum of the angles is : =\ 50^{\circ}\ +\ 130^{\circ}\ =\ 180^{\circ} . Hence the angles are supplementary to each other.

(iv) Sum of the angles is : =\ 45^{\circ}\ +\ 45^{\circ}\ =\ 90^{\circ} . Thus the angles are not supplement to each other.

NCERT Solutions for Maths Chapter 5 Lines and Angles Class 7 Topic 5.2.3

1. Can two adjacent angles be supplementary?

Answer: Yes, two adjacent angles can be supplementary.

For e.g., 40^{\circ} and 140^{\circ} can be two adjacent angles which are supplementary angles.

2. Can two adjacent angles be complementary?

Answer: Yes, two adjacent angles can be complementary to each other.

For e.g., adjacent angles 40^{\circ} and 50^{\circ} are complementary angles.

3. Can two obtuse angles be adjacent angles?

Answer: Yes, two obtuse angles can be adjacent for e.g., 100^{\circ} and 150^{\circ} can be adjacent angles.

4. Can an acute angle be adjacent to an obtuse angle?

Answer: Yes, the acute angle can be adjacent to an obtuse angle.

For e.g., 20^{\circ} and 120^{\circ} can be adjacent angles.

1. Are the angles marked 1 and 2 adjacent? (Fig). If they are not adjacent, say, ‘why’.

02

Answer: The condition for being adjacent angles are:-

(a) they have a common vertex

(b) they have common arm

Hence in the given figures:-

(i) These angles are adjacent angles as they agree above conditions.

(ii) The angles are adjacent angles.

(iii) These angles are not adjacent as their vertices are different.

(iv) These are adjacent angles.

(v) The angles are adjacent angles.

2. In the given Fig , are the following adjacent angles?

(a) \angle AOB and \angle BOC
(b) \angle BOD and \angle BOC

Justify your answer.

03

Answer: (a) \angle AOB and \angle BOC are adjacent angles as they have common vertex and share a common arm.

(b) \angle BOD and \angle BOC are not adjacent angles as \angle BOC is contained in \angle BOD .

NCERT Solutions for C lass 7 Maths Chapter 5 Lines and Angles Topic 5.2.4

1. Can two acute angles form a linear pair?

Answer: No two acute angles cannot form a linear pair. As the sum of angles in the linear pair is 180^{\circ} .

But the acute angles have their maximum value of 90^{\circ} thus their sum cannot be 180^{\circ} .

2. Can two obtuse angles form a linear pair?

Answer: No two obtuse angles cannot form a linear pair as their sum will exceed 180^{\circ} , but the sum of angles in linear pair is 180^{\circ} .

3. Can two right angles form a linear pair?

Answer: Yes, two right angles will form a linear pair as their sum is 180^{\circ} which is the sum of angles in linear pair.

1. Check which of the following pairs of angles form a linear pair (Fig):

1643866798868

Answer: The sum angles of linear pair is 180^{\circ} .

(i) Sum of the given angles is : =\ 40^{\circ}\ +\ 140^{\circ}\ =\ 180^{\circ} . Thus these are linear pair.

(ii) Sum of the given angles is : =\ 60^{\circ}\ +\ 60^{\circ}\ =\ 120^{\circ} . Thus these are not linear pair.

(iii) Sum of the given angles is : =\ 90^{\circ}\ +\ 80^{\circ}\ =\ 170^{\circ} . Thus these are not a linear pair.

(iv) Sum of the given angles is : =\ 115^{\circ}\ +\ 65^{\circ}\ =\ 180^{\circ} . Thus these are linear pair.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.2.5

1. In the given figure, if \angle 1=30^{o} , find \angle 2 and \angle 3 .

1643866863659

Answer: From the given figure :

(a) \angle 1\ =\ \angle 3\ =\ 30^{\circ} (Vertically opposite angles)

(b) \angle 2\ =\ 180^{\circ}\ -\ \angle 1\ =\ 150^{\circ} (Linear pair)

2. Give an example for vertically opposite angles in your surroundings.

Answer: The very common example of vertically opposite angle is scissors. Its arms form vertically opposite angles.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.3.1

1. Find examples from your surroundings where lines intersect at right angles.

Answer: The floor and the pillars in the house are at the right angle. Apart from this, the walls are perpendicular to the floor.

3. Draw any rectangle and find the measures of angles at the four vertices made by the intersecting lines.

Answer: We know that the opposite sides of the rectangle are equal and parallel to each other.

Then for two interior angles on the same side of the transversal, we can write :

\angle A\ +\ \angle B\ =\ 180^{\circ}

Also, \angle A\ =\ \angle B (Since opposite sides are equal)

Thus \angle A\ =\ \angle B\ =\ 90^{\circ}

4. If two lines intersect, do they always intersect at right angles?

Answer: No, it is not necessary that lines always intersect at right angles. The lines may form an acute angle (another angle will be obtuse as to form a linear pair).

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Topic 5.3.2

1. Suppose two lines are given. How many transversals can you draw for these lines?

Answer: We can draw infinite transversals from these two lines.

2. If a line is a transversal to three lines, how many points of intersections are there?

Answer: We know that transversal cuts lines at distinct points. Thus if a transversal cuts 3 lines then it will have 3 intersecting points.

3. Try to identify a few transversals in your surroundings.

Answer: Few examples of the transversal are road crossing of different railway line crossing the other lines. Transversal intersects lines at a distinct point.

1.(i) Name the pairs of angles in each figure:

1643866903425

(i)

Answer: The given pair of angles are corresponding angles.

1.(ii) Name the pairs of angles in each figure:

1643866941544

(ii)

Answer: The given pair of angles are alternate interior angles.

1.(iii) Name the pairs of angles in each figure:

015

Answer: The angles shown are pair of interior angles.

1.(iv) Name the pairs of angles in each figure:

017

Answer: These are a pair of corresponding angles.

1.(v) Name the pairs of angles in each figure:

1643866978318

(v)

Answer: The angles shown are pair of alternate interior angles.

1.(vi) Name the pairs of angles in each figure:

020

Answer: The given angles are linear pairs of angles as they form a straight line.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.1

1.(i) Find the complement of each of the following angles:

04

Answer: The sum of the complementary angle is 90^{\circ} .

Thus the complementary angle to the given angle is : =\ 90^{\circ}\ -\ 20^{\circ}\ =\ 70^{\circ}

1.(ii) Find the complement of each of the following angles:

05

Answer: The sum of the complementary angle is 90^{\circ} .

Thus the complementary angle to the given angle is : =\ 90^{\circ}\ -\ 63^{\circ}\ =\ 27^{\circ}

1.(iii) Find the complement of each of the following angles:

06

Answer: The sum of the complement angles is 90^{\circ} .

Thus the complement of the angle is given by : =\ 90^{\circ}\ -\ 57^{\circ}\ =\ 33^{\circ}

2.(i) Find the supplement of each of the following angles:

014

Answer: We know that sum of supplement angles is 180^{\circ}

The supplement of the given angle is : =\ 180^{\circ}\ -\ 105^{\circ}\ =\ 75^{\circ}

2.(ii) Find the supplement of each of the following angles:

1643867078109

Answer: We know that the sum of angles of supplementary pair is 180^{\circ} .

Thus the supplement of the given angle is : =\ 180^{\circ}\ -\ 87^{\circ}\ =\ 93^{\circ}

2.(iii) Find the supplement of each of the following angles:

1643867109355

Answer: We know that the sum of angles of supplementary pair is 180^{\circ} .

Thus the supplement of the given angle is :

=\ 180^{\circ}\ -\ 154^{\circ}\ =\ 26^{\circ}


3. Identify which of the following pairs of angles are complementary and which are supplementary.

(i) 65^{o},115^{o} (ii) 63^{o}, 27^{o} (iii) 112^{o}, 68^{o}

(iv) 130^{o}, 50^{o} (v) 45^{o}, 45^{o} (vi) 80^{o}, 10^{o}

Answer: We know that the sum of supplementary angles is 180^{\circ} and the sum of complementary angle is 90^{\circ} .

(i) Sum of the angles is : 65^{\circ}\ +\ 115^{\circ}\ =\ 180^{\circ} . Hence these are supplementary angles.

(ii) Sum of the angles is : 63^{\circ}\ +\ 27^{\circ}\ =\ 90^{\circ} . Hence these are complementary angles.

(iii) Sum of the angles is : 112^{\circ}\ +\ 68^{\circ}\ =\ 180^{\circ} . Hence these are supplementary angles.

(iv) Sum of the angles is : 130^{\circ}\ +\ 50^{\circ}\ =\ 180^{\circ} . Hence these are supplementary angles.

(v) Sum of the angles is : 45^{\circ}\ +\ 45^{\circ}\ =\ 90^{\circ} . Hence these are complementary angles.

(vi) Sum of the angles is : 80^{\circ}\ +\ 10^{\circ}\ =\ 90^{\circ} . Hence these are complementary angles.

4. Find the angle which is equal to its complement.

Answer: Let the required angle be \Theta .

Then according to question, we have :

\Theta\ +\ \Theta\ =\ 90^{\circ}

or 2\Theta\ =\ 90^{\circ}

or \Theta\ =\ 45^{\circ}

5. Find the angle which is equal to its supplement.

Answer: Let the required angle be \Theta .

Then according to the question :

\Theta\ +\ \Theta \ =\ 180^{\circ}

or 2\Theta \ =\ 180^{\circ}

or \Theta \ =\ 90^{\circ}

Hence the angle is 90^{\circ} .

6. In the given figure, \angle 1 and \angle 2 are supplementary angles. If \angle 1 is decreased, what changes should take place in \angle 2 so that both the angles still remain supplementary.

013

Answer: Since it is given that \angle 1 and \angle 2 are supplementary angles, i.e. the sum of both angles is 180^{\circ} .

Thus if \angle 1 is decreased then to maintain the sum \angle 2 needs to be increased.

7. Can two angles be supplementary if both of them are:

(i) acute ? (ii) obtuse ? (iii) right ?

Answer: We know that the sum of supplementary angles is 180^{\circ} .

(i) The maximum value of the sum of two acute angles is less than 180^{\circ} . Thus two acute angles can never be supplementary.

(ii) The minimum value of the sum of two obtuse angles is more than 180^{\circ} . Thus two obtuse angles can never be supplementary.

(iii) Sum of two right angles is 180^{\circ} . Hence two right angles are supplementary.

8. An angle is greater than 45^{o} . Is its complementary angle greater than 45^{o} or equal to 45^{o} or less than 45^{o} ?

Answer: We know that the sum of two complementary angles is 90^{\circ} .

Thus if one of the angles is greater than 45^{\circ} then the other angle needs to be less than 45^{\circ} .

9. In the adjoining figure:

(i) Is \angle 1 adjacent to \angle 2 ?
(ii) Is \angle AOC adjacent to \angle AOE ?

(iii) Do \angle COE and \angle EOD form a linear pair?
(iv) Are \angle BOD and \angle DOA supplementary?
(v) Is \angle 1 vertically opposite to \angle 4 ?
(vi) What is the vertically opposite angle of \angle 5 ?

012

Answer: (i) Yes, \angle 1 adjacent to \angle 2 as these have the same vertex and have one common arm.

(ii) No, \angle AOC is not adjacent to \angle AOE . This is because \angle AOE contains \angle AOC .

(iii) Yes the given angles form a linear pair as they are pair of supplementary angles.

(iv) Since BOA is a straight line thus the given angles are supplementary.

(v) Yes, \angle 1 and \angle 4 are vertically opposite angles as they are the angles formed by two intersecting straight lines.

(vi) The vertically opposite angle to \angle 5 is \left ( \angle 2\ +\ \angle 3 \right ) .

10. (i) Indicate which pairs of angles are:

(i) Vertically opposite angles.

023

Answer: The vertically opposite pairs are :

(a) \angle 1 and \angle 4

(b) \angle 5 and \left ( \angle 2\ +\ \angle 3 \right )

10.(ii) Indicate which pairs of angles are:

(ii) Linear pairs

010

Answer: The sum of angles in linear pair is 180^{\circ} .

Thus the linear pairs are :

(a) \angle 1\ and\ \angle 5

(b) \angle 4\ and\ \angle 5

11. In the following figure, is \angle 1 adjacent to \angle 2 ? Give reasons.

011

Answer: No, \angle 1 and \angle 2 are not adjacent angles as their vertex is not same/common.

For being adjacent angles the pair must have a common vertex and have a common arm.


12.(i) Find the values of the angles x, y, and z in each of the following:

09

Answer: From the figure :

(i) \angle x\ =\ 55^{\circ} (Vertically opposite angle)

(ii) \angle y\ =\ 180^{\circ}\ -\ 55^{\circ}\ =\ 125^{\circ} (Linear pair)

(iii) \angle y\ =\ \angle z\ =\ 125^{\circ} (Vertically opposite angle)

12.(ii) Find the values of the angles x, y, and z in each of the following:

1643867159703

Answer: From the figure we can observe that :

(i) \angle z\ =\ 40^{\circ} (Vertically opposite angle)

(ii) \angle x\ =\ 180^{\circ}\ -\ 40^{\circ}\ -\ 25^{\circ}\ =\ 115^{\circ} (Linear pair/straight line)

(iii) \angle y\ =\ 180^{\circ}\ -\ \angle z\ =\ 140^{\circ} (Vertically opposite angle).

13. Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

(ii) If two angles are supplementary, then the sum of their measures is ______.

(iii) Two angles forming a linear pair are _______________.

(iv) If two adjacent angles are supplementary, they form a ___________.

(v) If two lines intersect at a point, then the vertically opposite angles are always _____________.

(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are __________.

Answer: (i) 90^{\circ}

(ii) 180^{\circ}

(iii) Supplementary angles

(iv) Straight line

(v) equal

(vi) obtuse angles (as they form a line).

14. In the adjoining figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles
(ii) Adjacent complementary angles
(iii) Equal supplementary angles
(iv) Unequal supplementary angles
(v) Adjacent angles that do not form a linear pair

08

Answer: (i) \angle AOD\ and\ \angle BOC are the vertically obtuse angles.

(ii) \angle AOB\ and\ \angle AOE are the complementary angles.

(iii) \angle BOE\ and\ \angle DOE are the equal supplementary angles.

(iv) \angle BOC\ and\ \angle COD are the unequal pair of supplementary angle.

(v) \angle AOB\ and\ \angle AOE , \angle EOD\ and\ \angle COD and \angle AOE\ and\ \angle EOD are adjacent angles but are not supplementary angles.


NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Exercise 5.2

1.(i) State the property that is used in each of the following statements?

(i) If a\parallel b , then \angle 1= \angle 5 .

07

Answer: The statement "If a\parallel b , then \angle 1= \angle 5 " is true using the corresponding angles property .

1.(ii) State the property that is used in each of the following statements?

(ii) If \angle 4=\angle 6 , then a\parallel b.

07

Answer: The property used here is 'alternate interior angle property'.

(iii) If \angle 4+\angle 5= 180^{o} , then a\parallel b.
07

Answer: The property used here is ' Interior angles on the same side of the transversal are a pair of supplementary angles '.


2. In the adjoining figure, identify

(i) the pairs of corresponding angles.
(ii) the pairs of alternate interior angles.
(iii) the pairs of interior angles on the same side of the transversal.
(iv) the vertically opposite angles.

016


Answer: (i) Corresponding angles :- \angle 1\ and\ \angle 5 , \angle 2\ and\ \angle 6 , \angle 3\ and\ \angle 7 , \angle 4\ and\ \angle 8

(ii) Alternate interior angles :- \angle 2\ and\ \angle 8 , \angle 3\ and\ \angle 5 ,

(iii) Alternate angles on the same side of traversal :- \angle 2\ and\ \angle 5 , \angle 3\ and\ \angle 8

(iv) Vertically opposite angles :- \angle 1\ and\ \angle 3 , \angle 2\ and\ \angle 4 , \angle 5\ and\ \angle 7 , \angle 6\ and\ \angle 8

3. In the adjoining figure, p\parallel q . Find the unknown angles.

018

Answer: The angles can be found using different properties:

(a) \angle e\ =\ 180^{\circ}\ -\ 125^{\circ}\ =\ 55^{\circ} (The angles are linear pair)

(b) \angle e\ =\ \angle f\ =\ 55^{\circ} (Vertically opposite angle)

(c) \angle d\ =\ 125^{\circ} (Corresponding angle)

(d) \angle d\ =\ \angle b\ =\ 125^{\circ} (Vertically opposite angle)

(e) \angle a\ =\ \angle c\ =\ 180^{\circ}\ -\ 125^{\circ}\ =\ 55^{\circ} (Vertically opposite angel, linear pair).

4.(i) Find the value of x in each of the following figures if l\parallel m .

019

Answer: The linear pair of the 110^{\circ} is : \Theta \ =\ 180^{\circ}\ -\ 110^{\circ}\ =\ 70^{\circ}

Thus the value of x is : x\ =\ 70^{\circ} (Corresponding angles of parallel lines are equal).

4.(ii) Find the value of x in each of the following figures if l\parallel m.

021

Answer: The value of x is 100^{\circ} , as these are the corresponding angles.

5. In the given figure, the arms of two angles are parallel. If \angle ABC= 70^{o} , then find

(i) \angle DGC

(ii)\angle DEF

022

Answer: (i) Since side AB is parallel to DG.

Thus : \angle DGC\ =\ 70^{\circ} (Corresponding angles of parallel arms are equal.)

(ii) Further side BC is parallel to EF.

We have : \angle DEF\ =\ \angle DGC\ =\ 70^{\circ} (Corresponding angles of parallel arms are equal.)

6. In the given figures below, decide whether l is parallel to m .

1643867198020 Answer: (i) In this case. the sum of the interior angle is 126^{\circ}\ +\ 44^{\circ}\ =\ 170^{\circ} thus l is not parallel to m.\

(ii) In this case, also l is not parallel to m as the corresponding angle cannot be 75^{\circ} (Linear pair will not form).

(iii) In this l and m are parallel. This is because the corresponding angle is 57^{\circ} and it forms linear pair with 123^{\circ} .

(iv) The lines are not parallel as the linear pair not form. (Since the corresponding angle will be 72^{\circ} otherwise.)

Lines and Angles Class 7 Maths Chapter 5-Topics

  • Related Angles
  • Pairs Of Lines
  • Checking For Parallel Lines

NCERT Solutions for Class 7 Maths Chapter Wise

Chapter No.

Chapter Name

Chapter 1

Integers

Chapter 2

Fractions and Decimals

Chapter 3

Data Handling

Chapter 4

Simple Equations

Chapter 5

Lines and Angles

Chapter 6

The Triangle and its Properties

Chapter 7

Congruence of Triangles

Chapter 8

Chapter 9

Rational Numbers

Chapter 10

Practical Geometry

Chapter 11

Perimeter and Area

Chapter 12

Algebraic Expressions

Chapter 13

Exponents and Powers

Chapter 14

Symmetry

Chapter 15

NCERT Solutions for Class 7 Subject Wise

Benefits of NCERT solutions for Class 7 Maths chapter 5 Lines and Angles:

  • Solving homework is an easy task with solutions of NCERT Class 7 Maths chapter 5 Lines and Angles in hand.
  • Questions of similar type from CBSE NCERT solutions for Class 7 Maths chapter 5 are expected for the Class exams.
  • Practice all the questions from NCERT solutions for Class 7 Maths chapter 5 Lines and Angles to score well in the exam.

Also Check NCERT Books and NCERT Syllabus here:

Frequently Asked Question (FAQs)

1. Why we study lines and angles?

Lines and angles which are discussed in chapter 5 maths class 7 are the basics of geometry. It will be definitely useful in higher studies. Not only in mathematics but in almost all the subjects. Students can download lines and angles class 7 pdf to study both online and offline. 

2. What are the topics covered in NCERT Class 7 Maths Chapter 5

Here are the topics are covered in NCERT solution Class 7 chapter 5

  • Related Angles
  • Pairs Of Lines 
  • Checking For Parallel Lines

Students can study lines and angles class 7 pdf  both online and offline. 

3. Write the different types of angles

Following is a list of different types of angles that are discussed in NCERT Maths class 7 chapter 5  

  • Acute Angles.
  • Obtuse Angles.
  • Right Angles.
  • Straight Angles.
  • Reflex Angles.
  • Full Rotation.

Students can find these concepts in lines and angles class 7 pdf which can be downloaded form official website of Careers360.

4. What are complementary and supplementary angles discussed in NCERT maths class 7 chapter 5

According to NCERT maths class 7 chapter 5:

  • Complementary angles are two angles whose sum is 90 degrees. In other words, they "complete" each other to form a right angle.
  • Supplementary angles are two angles whose sum is 180 degrees. They form a straight line when placed next to each other.
5. What's the difference between adjacent and linear pairs of angles?

According to chapter 5 class 7 maths the difference between adjacent and linear pairs of angles is:

  • Adjacent angles share a common vertex and a common side but don't overlap. They are side by side.
  • Linear pairs are adjacent angles that form a straight line when combined. The sum of their measures is always 180 degrees.

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Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

Bio Medical Engineer

The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary. 

4 Jobs Available
Data Administrator

Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.

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Ethical Hacker

A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.

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Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

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Geothermal Engineer

Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.

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Remote Sensing Technician

Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive. 

Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.

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Geotechnical engineer

The role of geotechnical engineer starts with reviewing the projects needed to define the required material properties. The work responsibilities are followed by a site investigation of rock, soil, fault distribution and bedrock properties on and below an area of interest. The investigation is aimed to improve the ground engineering design and determine their engineering properties that include how they will interact with, on or in a proposed construction. 

The role of geotechnical engineer in mining includes designing and determining the type of foundations, earthworks, and or pavement subgrades required for the intended man-made structures to be made. Geotechnical engineering jobs are involved in earthen and concrete dam construction projects, working under a range of normal and extreme loading conditions. 

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Cartographer

How fascinating it is to represent the whole world on just a piece of paper or a sphere. With the help of maps, we are able to represent the real world on a much smaller scale. Individuals who opt for a career as a cartographer are those who make maps. But, cartography is not just limited to maps, it is about a mixture of art, science, and technology. As a cartographer, not only you will create maps but use various geodetic surveys and remote sensing systems to measure, analyse, and create different maps for political, cultural or educational purposes.

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Budget Analyst

Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.

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Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

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Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

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Investment Banker

An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.

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Underwriter

An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.

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Finance Executive
3 Jobs Available
Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

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Plumber

An expert in plumbing is aware of building regulations and safety standards and works to make sure these standards are upheld. Testing pipes for leakage using air pressure and other gauges, and also the ability to construct new pipe systems by cutting, fitting, measuring and threading pipes are some of the other more involved aspects of plumbing. Individuals in the plumber career path are self-employed or work for a small business employing less than ten people, though some might find working for larger entities or the government more desirable.

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Construction Manager

Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.

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Urban Planner

Urban Planning careers revolve around the idea of developing a plan to use the land optimally, without affecting the environment. Urban planning jobs are offered to those candidates who are skilled in making the right use of land to distribute the growing population, to create various communities. 

Urban planning careers come with the opportunity to make changes to the existing cities and towns. They identify various community needs and make short and long-term plans accordingly.

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Highway Engineer

Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

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Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems. 

2 Jobs Available
Naval Architect

A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability. 

2 Jobs Available
Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

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A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

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Speech Therapist
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Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth. 

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Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

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Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

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Hospital Administrator

The hospital Administrator is in charge of organising and supervising the daily operations of medical services and facilities. This organising includes managing of organisation’s staff and its members in service, budgets, service reports, departmental reporting and taking reminders of patient care and services.

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Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

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Acrobat

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Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

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Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

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Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

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Videographer
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Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

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Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

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Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

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Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

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Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

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Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

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Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

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Linguist

Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning). 

Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian

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Public Relation Executive
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Travel Journalist

The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.

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Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
QA Manager
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Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Production Manager
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Merchandiser
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QA Lead

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans. 

2 Jobs Available
Metallurgical Engineer

A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment. 

2 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
QA Manager
4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
ITSM Manager
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Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
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