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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.
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:
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.
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 and are complementary angle as their sum is .
2. Can two obtuse angles be complement to each other?
Answer:
Since obtuse angles are greater than . Thus two obtuse angles cannot be a complement to each other. (as the sum of complementary angles is .)
3. Can two right angles be complement to each other?
Answer: The sum of angles in complementary angles is . 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 :
Thus two angles are complementary to each other.
1.(ii) Which pairs of following angles are complementary?
Answer: The sum of the two angles is :
In complementary angles sum of the angles is . Hence given pair of angles are not complementary.
1. (iii) Which pairs of the following angles are complementary?
Answer: We know that the sum angles of complementary angles is .
In the given figure: Sum of angles is
Hence given pair of angles are not complementary.
1.(iv) Which pairs of following angles are complementary?
Answer: The sum of the two angles is :
In complementary angles sum of the angles is . 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?
Answer: We know that the sum of complementary angles is .
Thus the complement of the given angle is :
2.(ii) What is the measure of the complement of each of the following angles?
Answer: The sum of complementary angles are .
Thus the required angle is :
2.(iii) What is the measure of the complement of each of the following angles?
Answer: We know that the sum of complementary angles is .
Hence the required complement of the given angle is :
2.(iv) What is the measure of the complement of each of the following angles?
Answer: We know that the sum of complementary angles is .
Hence the complement of the given angle is :
3. The difference in the measures of two complementary angles is . Find the measures of the angles.
Answer: Let one of the angles be .
It is given that the angles are complementary to each other. So the other angle will be .
Further, it is given that the difference of the angle is 12.
So the equation is :
or
or
Hence the two angles are and .
1. Can two obtuse angles be supplementary?
Answer: No, two obtuse angles cannot be supplementary as their the sum of angles will exceed .
2. Can two acute angles be supplementary?
Answer: No two acute angles cannot be supplementary.
For being the supplementary angles their sum should be .
But the acute angles are less than . Hence their maximum doesn't reach .
3. Can two right angles be supplementary?
Answer: Yes, two right angles are supplementary as their sum is .
1. Find the pairs of supplementary angles in Fig :
Answer: We know that the sum of the supplementary angle is .
(i) Sum of the angles is : . Hence the angles are not supplementary.
(ii) Sum of the angles is : . Thus the angles are not supplementary.
(iii) Sum of the angles is : . Hence the angles are supplementary to each other.
(iv) Sum of the angles is : . Thus the angles are not supplement to each other.
1. Can two adjacent angles be supplementary?
Answer: Yes, two adjacent angles can be supplementary.
For e.g., and 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 and are complementary angles.
3. Can two obtuse angles be adjacent angles?
Answer: Yes, two obtuse angles can be adjacent for e.g., and 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., and 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) and
(b) and
Justify your answer.
Answer: (a) and are adjacent angles as they have common vertex and share a common arm.
(b) and are not adjacent angles as is contained in .
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 .
But the acute angles have their maximum value of thus their sum cannot be .
2. Can two obtuse angles form a linear pair?
Answer: No two obtuse angles cannot form a linear pair as their sum will exceed , but the sum of angles in linear pair is .
3. Can two right angles form a linear pair?
Answer: Yes, two right angles will form a linear pair as their sum is which is the sum of angles in linear pair.
1. Check which of the following pairs of angles form a linear pair (Fig):
Answer: The sum angles of linear pair is .
(i) Sum of the given angles is : . Thus these are linear pair.
(ii) Sum of the given angles is : . Thus these are not linear pair.
(iii) Sum of the given angles is : . Thus these are not a linear pair.
(iv) Sum of the given angles is : . Thus these are linear pair.
1. In the given figure, if , find and .
Answer: From the given figure :
(a) (Vertically opposite angles)
(b) (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.
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.
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 :
Also, (Since opposite sides are equal)
Thus
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).
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:
(i)
Answer: The given pair of angles are corresponding angles.
1.(ii) Name the pairs of angles in each figure:
(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.(v) Name the pairs of angles in each figure:
(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 pairs of angles as they form a straight line.
1.(i) Find the complement of each of the following angles:
Answer: The sum of the complementary angle is .
Thus the complementary angle to the given angle is :
1.(ii) Find the complement of each of the following angles:
Answer: The sum of the complementary angle is .
Thus the complementary angle to the given angle is :
1.(iii) Find the complement of each of the following angles:
Answer: The sum of the complement angles is .
Thus the complement of the angle is given by :
2.(i) Find the supplement of each of the following angles:
Answer: We know that sum of supplement angles is
The supplement of the given angle is :
2.(ii) Find the supplement of each of the following angles:
Answer: We know that the sum of angles of supplementary pair is .
Thus the supplement of the given angle is :
2.(iii) Find the supplement of each of the following angles:
Answer: We know that the sum of angles of supplementary pair is .
Thus the supplement of the given angle is :
3. Identify which of the following pairs of angles are complementary and which are supplementary.
Answer: We know that the sum of supplementary angles is and the sum of complementary angle is .
(i) Sum of the angles is : . Hence these are supplementary angles.
(ii) Sum of the angles is : . Hence these are complementary angles.
(iii) Sum of the angles is : . Hence these are supplementary angles.
(iv) Sum of the angles is : . Hence these are supplementary angles.
(v) Sum of the angles is : . Hence these are complementary angles.
(vi) Sum of the angles is : . Hence these are complementary angles.
4. Find the angle which is equal to its complement.
Answer: Let the required angle be .
Then according to question, we have :
or
or
5. Find the angle which is equal to its supplement.
Answer: Let the required angle be .
Then according to the question :
or
or
Hence the angle is .
6. In the given figure, and are supplementary angles. If is decreased, what changes should take place in so that both the angles still remain supplementary.
Answer: Since it is given that and are supplementary angles, i.e. the sum of both angles is .
Thus if is decreased then to maintain the sum 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 .
(i) The maximum value of the sum of two acute angles is less than . Thus two acute angles can never be supplementary.
(ii) The minimum value of the sum of two obtuse angles is more than . Thus two obtuse angles can never be supplementary.
(iii) Sum of two right angles is . Hence two right angles are supplementary.
8. An angle is greater than . Is its complementary angle greater than or equal to or less than ?
Answer: We know that the sum of two complementary angles is .
Thus if one of the angles is greater than then the other angle needs to be less than .
(i) Is adjacent to ?
(ii) Is adjacent to ?
(iii) Do and form a linear pair?
(iv) Are and supplementary?
(v) Is vertically opposite to ?
(vi) What is the vertically opposite angle of ?
Answer: (i) Yes, adjacent to as these have the same vertex and have one common arm.
(ii) No, is not adjacent to . This is because contains .
(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, and are vertically opposite angles as they are the angles formed by two intersecting straight lines.
(vi) The vertically opposite angle to is .
10. (i) Indicate which pairs of angles are:
(i) Vertically opposite angles.
Answer: The vertically opposite pairs are :
(a) and
(b) and
10.(ii) Indicate which pairs of angles are:
(ii) Linear pairs
Answer: The sum of angles in linear pair is .
Thus the linear pairs are :
(a)
(b)
11. In the following figure, is adjacent to ? Give reasons.
Answer: No, and 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) (Vertically opposite angle)
(ii) (Linear pair)
(iii) (Vertically opposite angle)
12.(ii) Find the values of the angles x, y, and z in each of the following:
Answer: From the figure we can observe that :
(i) (Vertically opposite angle)
(ii) (Linear pair/straight line)
(iii) (Vertically opposite angle).
(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)
(ii)
(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
Answer: (i) are the vertically obtuse angles.
(ii) are the complementary angles.
(iii) are the equal supplementary angles.
(iv) are the unequal pair of supplementary angle.
(v) , and are adjacent angles but are not supplementary angles.
1.(i) State the property that is used in each of the following statements?
(i) If , then .
Answer: The statement "If , then " is true using the corresponding angles property .
1.(ii) State the property that is used in each of the following statements?
(ii) If , then
Answer: The property used here is 'alternate interior angle property'.
(iii) If , then
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 :- , , ,
(ii) Alternate interior angles :- , ,
(iii) Alternate angles on the same side of traversal :- ,
(iv) Vertically opposite angles :- , , ,
3. In the adjoining figure, . Find the unknown angles.
Answer: The angles can be found using different properties:
(a) (The angles are linear pair)
(b) (Vertically opposite angle)
(c) (Corresponding angle)
(d) (Vertically opposite angle)
(e) (Vertically opposite angel, linear pair).
4.(i) Find the value of in each of the following figures if .
Answer: The linear pair of the is :
Thus the value of x is : (Corresponding angles of parallel lines are equal).
4.(ii) Find the value of in each of the following figures if
Answer: The value of x is , as these are the corresponding angles.
5. In the given figure, the arms of two angles are parallel. If , then find
Answer: (i) Since side AB is parallel to DG.
Thus : (Corresponding angles of parallel arms are equal.)
(ii) Further side BC is parallel to EF.
We have : (Corresponding angles of parallel arms are equal.)
6. In the given figures below, decide whether is parallel to .
Answer: (i) In this case. the sum of the interior angle is thus l is not parallel to m.\
(ii) In this case, also l is not parallel to m as the corresponding angle cannot be (Linear pair will not form).
(iii) In this l and m are parallel. This is because the corresponding angle is and it forms linear pair with .
(iv) The lines are not parallel as the linear pair not form. (Since the corresponding angle will be otherwise.)
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | Lines and Angles |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
Also Check NCERT Books and NCERT Syllabus here:
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.
Here are the topics are covered in NCERT solution Class 7 chapter 5
Students can study lines and angles class 7 pdf both online and offline.
Following is a list of different types of angles that are discussed in NCERT Maths class 7 chapter 5
Students can find these concepts in lines and angles class 7 pdf which can be downloaded form official website of Careers360.
According to NCERT maths class 7 chapter 5:
According to chapter 5 class 7 maths the difference between adjacent and linear pairs of angles is:
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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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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