NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

 

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 class 6. In this chapter, we deal with lines, different kinds of angles and their measurements. There are  2 exercises with 20 questions in this chapter. The solutions of NCERT class 7 maths chapter 5 lines and angles give an explanation to all these questions. The CBSE NCERT solutions for class 7 maths chapter 5 lines and angles are extremely helpful for the students to understand the basics of this chapter and to clear all their doubts easily. These NCERT Solutions are given here with a step-by-step explanation of each and every problem of NCERT textbook. This chapter is all about the lines and angles. In this chapter students always confuse 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. Thus, in other words, we can say that a line has no endpoints. A ray has only one endpoint which is its initial point. An angle is formed when line segments or lines meet. 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 solutions to two exercises of this chapter.

Exercise:5.1

Exercise:5.2

Important points of NCERT Class 7 Maths Chapter 5 Lines and Angles are-

Problems related to the following points are discussed in the NCERT solutions for class 7 maths chapter 5 lines and angles.

  • An angle is formed when two lines or line-segments or rays meet  

    Pairs of Angles

             Condition

Two complementary angles

Measures add up to 90^o

Two supplementary angles

Measures add up to 180^o

Two adjacent angles 

Have a common arm and a common vertex but no common interior

Linear pair

Adjacent and supplementary

  • When two lines l and m are intersected it means they both are meet at a point and the meeting point is called the point of intersection.

  • When two lines l and m drawn on a sheet of paper do not meet or intersect, however far produced, then this lines called as parallel lines.

  • When two lines intersect we have two pairs of opposite angles. They are called vertically opposite angles and both angles are equal in measure.

  • Transversal- It is a line that intersects two or more than two lines at distinct points. And it gives rise to several types of angles. For example interior angles, exterior angles, corresponding angles, alternate interior, and alternate exterior angles.

Topic-wise questions are also explained in the CBSE NCERT solutions for class 7 maths chapter 5 lines and angles.

Topics of NCERT Grade 7 Maths Chapter 5 Lines and Angles-

5.1 Introduction

5.2 Related Angles

5.2.1 Complementary Angles

5.2.2 Supplementary Angles

5.2.3 Adjacent Angles

5.2.4 Linear Pair

5.2.5 Vertically Opposite Angles

5.3 Pairs of Lines

5.3.1 Intersecting Lines

5.3.2 Transversal

5.3.3 Angles made by a Transversal

5.3.4 Transversal of Parallel Lines

5.4 Checking for Parallel Lines

Solutions for NCERT class 7 maths chapter 5 lines and angles topic 5.2.1

1. Can two acute angles be 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?

  

 

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?

 Which pairs of following angles are complementary

 

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 following angles are complementary?

  Which pairs of following angles are complementary(iii)

 

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?

 Which pairs of following angles are complementary(iv)

 

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}.

CBSE NCERT solutions for class 7 maths chapter 5 lines and angles 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  :

 Find the pairs of supplementary angles in Fig 5.7:

 

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. 

Solutions of NCERT class 7 maths chapter 5 lines and angles 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’.

 

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.

      

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.

Solutions for NCERT class 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):

 Check which of the following pairs of angles form a linear pair (Fig 5.13)

                 

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.

 

CBSE 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 .

   Lines and angles

 

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.

Solutions of NCERT  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 linear pair).

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:

Name the pairs of angles in each figure(i)

              (i)

Answer:

The given pair of angles are corresponding angles.

 

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

Name the pairs of angles in each figure(ii)

                        (ii)

Answer:

The given pair of angles are alternate interior angles.

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

 

Answer:

The angles shown are pair of interior angles.

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

Answer:

These are pair of corresponding angles.

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

           Name the pairs of angles in each figure(v)

                          (v)

Answer:

The angles shown are pair of alternate interior angles.

 

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

 

Answer:

The given angles are linear pair of angle 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:

 

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:

 

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:

   

 

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:

 

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:

 

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:

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.    

 

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 ?

                                                                                                                                                            

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.

 

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

 

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.

 

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:

 

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: 

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

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).

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

 

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.

 

 
 

CBSE 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.

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.

Answer:

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

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

 

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.

 

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.

  

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.

 

 

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.

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

  

 

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.

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

 

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.)  

NCERT Solutions for Class 7 Maths - Chapter-wise 

Chapter No.

Chapter Name

Chapter 1

Solutions of NCERT for class 7 maths chapter 1 Integers

Chapter 2

CBSE NCERT solutions for class 7 maths chapter 2 Fractions and Decimals

Chapter 3

NCERT solutions for class 7 maths chapter 3 Data Handling

Chapter 4

Solutions of NCERT for class 7 maths chapter 4 Simple Equations

Chapter 5

CBSE NCERT solutions for class 7 maths chapter 5 Lines and Angles

Chapter 6

NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties

Chapter 7

Solutions of NCERT for class 7 maths chapter 7 Congruence of Triangles

Chapter 8 NCERT solutions for class 7 maths chapter 8 comparing quantities

Chapter 9

CBSE NCERT solutions for class 7 maths chapter 9 Rational Numbers

Chapter 10

NCERT solutions for class 7 maths chapter 10 Practical Geometry

Chapter 11

Solutions of NCERT for class 7 maths chapter 11 Perimeter and Area

Chapter 12

CBSE NCERT solutions for class 7 maths chapter 12 Algebraic Expressions

Chapter 13

NCERT solutions for class 7 maths chapter 13 Exponents and Powers

Chapter 14

Solutions of NCERT for class 7 maths chapter 14 Symmetry

 NCERT Solutions for Class 7- Subject-wise 

Solutions of NCERT for class 7 maths

CBSE NCERT solutions for class 7 science

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.
 

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