# NCERT Solutions Class 7 Maths Chapter 5

## NCERT Solutions for Class 7 Mathematics Chapter 5 Lines and Angles

Chapter 5 Lines and Angles is considered to be one of the most  important chapters in Class 7 Mathematics. To help the students, Extramarks offers NCERT Solutions for Class 7 Mathematics Chapter 5, which are detailed solutions to the textbook exercises in this chapter.

Students can now refer to  answers to all difficult questions. These solutions are prepared by subject matter experts. They have provided explanations for all of the questions, keeping in mind the importance of this chapter in the final exams and the best answer pattern for solving the textbook questions are provided. There are many exercise problems for students to solve. Going through these solutions will help students with their preparations, last-minute revisions, and also help them with their assignments.

## NCERT Solutions for Class 7 Mathematics Chapter 5 Lines and Angles

[Solutions]

### NCERT Solutions for Class 7 Mathematics Chapter 5

NCERT Class 7 Mathematics Chapter 5 is Lines and Angles. This chapter has four major topics. To learn and relate to this important chapter in Mathematics, students are advised to go through the subtopics that are there in  this chapter.

The topics that are discussed in NCERT Solutions for Class 7 Mathematics Chapter 5 lines and angles are as follows:

• Introduction
• Related Angles
1. Complementary Angles
2. Supplementary Angles
4. Linear pairs
5. Vertically Opposite Angles
• Pairs of Lines
1. Intersecting Lines
2. Transversal
4. Transversal of Parallel Lines
• Checking for Parallel Lines

Extramarks recommends students study each of these topics carefully and then  turn to  the NCERT Solutions that are provided for the chapter on Lines and Angles.

### List of Exercises in Class 7 Mathematics Chapter 5

 Chapter 5 – Lines and Angles Exercises Exercise 5.1 Questions & Solutions Exercise 5.2 Questions & Solutions

### NCERT Solutions for Class 7 Mathematics Chapter 5 Lines and Angles

• Introduction

Students are introduced to this chapter with a recap of ray, line, line segment, and angle. A ray has no endpoints.  If it has an endpoint in one direction, we call it a line. A line segment has endpoints on both sides. When two lines or line segments intersect each other, an angle is formed.

Exercise 5.1 with 14 problems (4 are long answers, and 10 are short answers)

• Related Angles

Here, students will learn about different types of relative angles. Students can try to solve problems on each type of related angle so that it gives them knowledge about their properties too.

Exercise 5.2 with six sums (2 are short answers, 4 are long answers)

• Complementary Angles

In this section, students will learn complementary angles, properties, and other kinds. The law is that the sum of two complementary angles is 90 degrees. If an angle between two lines is 90 degrees, we can say one angle is  complementary  to another.

• Supplementary Angles

The next relative angle  is  supplementary angle. Contrary to the complementary aspects, the sum of the two angles is 180 degrees. Then they are called supplementary angles.

If any two angles have a common vertex and arm on any one side, they are called adjacent angles. The pages in a book, and the car stereo are the best examples of adjacent angles.

• Linear Pairs

In this section, students will come across the concepts of Linear Pairs. A pair of adjacent angles having rays in their non-common sides are nothing but linear pairs.

• Vertically Opposite Angles

The angles formed between the metal blades and handles of a pair of scissors, laundry stands, etc., are the examples given to learn about vertically opposite angles. Students will experiment with pencils to learn more about these angles. When the two lines are intersecting each other, two equal and opposite angles are formed in a vertical direction.

• Pairs of Lines

In this segment, students of Class 7 will learn about lines, its types and properties with examples and explanations.

• Intersecting Lines

The first concept that the students will have to learn is intersecting lines. If two lines touch each other or meet at a certain point, those lines are called intersecting lines and the point where they meet is called the point of intersection.

• Transversal

It is an extension of intersecting lines. If two or more lines intersect at more than one point it is called a transversal. Students will understand them with examples like railway lines and cross multiple roads.

In this section, students can learn the interrelation between lines and angles. When two lines act as transversal, students can observe eight kinds of different angles formed with these lines. All the angles are different from each other. Some are interior, exterior, adjacent angles, and even corresponding angles.

• Transversal of Parallel Lines

In this topic, students will come to know the variations of parallel lines if they are transversal. If transversal cuts two parallel lines, each pair of corresponding angles and alternate interior angles are equal. Also, the pair of interior angles on the transversal side are supplementary to each other. So, a simple intersection can create so many angles and can change their properties.

• Checking for Parallel Lines

So far, students have learned to find angles based on lines. Now, students can try to learn about the lines based on the angles formed, i.e., vice versa of the previous topic. If two lines are transversal and the corresponding angles are equal, then the lines are parallel to each other.

## Key Features of NCERT Class 7 Mathematics Chapter 5

NCERT Solutions for Class 7 Mathematics Chapter 5 are easily accessible from Extramarks. The key features include:

• The NCERT Solutions are well explained and provide detailed understanding of the topic by the experienced faculty who meticulously follow the CBSE examination guidelines.
• Our solutions are compiled in an easy-to-understand and simple language so as to help students prepare for their exams and by guiding them  to solve the different kinds of problems in a step-by-step manner.
• It enhances students’ confidence to answer questions in the final exam.
• Students can also use these NCERT Solutions to prepare for other competitive exams.

### NCERT Solutions for Class 7 Mathematics

Students who find it difficult to answer the textbook questions can follow the NCERT Solutions provided by Extramarks. NCERT Solutions for Class 7 Mathematics has all the solved answers to the exercises in Class 7 Mathematics. The solutions are given in a   simple and comprehensive manner which makes it easier for students to understand and perform better.

## NCERT Solutions for Class 7

Apart from Mathematics, Class 7 students can also find NCERT solutions for other subjects including Science, Social Science, and English on Extramarks official website. Students can use these resources  to prepare more effectively and efficiently. Since most of the final exam questions are based on the same pattern as NCERT questions,  these solutions will come handy before the exams and will guarantee students higher scores.

NCERT Solutions Class 7 Maths Chapter-wise List

Q.1

$\mathrm{Find}\mathrm{the}\mathrm{complement}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{angles}:$ Ans.

$\begin{array}{l}\text{(i) 20}°\\ \text{Since the sum of complementary angle is 90}°\\ \text{So, we have}\\ \text{Complement}=\text{90}°-20°=\overline{)70°}\\ \text{(ii) 63}°\\ \text{Since the sum of complementary angle is 90}°\\ \text{So, we have}\\ \text{Complement}=\text{90}°-63°=\overline{)27°}\\ \text{(iii) 57}°\\ \text{Since the sum of complementary angle is 90}°\\ \text{So, we have}\\ \text{Complement}=\text{90}°-57°=\overline{)33°}\end{array}$

Q.2 Find the supplement of the following angles: Ans.

$\begin{array}{l}\text{(i) 105}°\\ \text{Since the sum of supplementary angle is 180}°\\ \text{So, we have}\\ \text{Complement}=\text{180}°-105°=\overline{)75°}\\ \text{(ii) 87}°\\ \text{Since the sum of Supplementary angle is 180}°\\ \text{So, we have}\\ \text{Complement}=\text{180}°-87°=\overline{)93°}\text{(iii) 154}°\\ \text{Since the sum of Supplementary angle is 180}°\\ \text{So, we have}\\ \text{Complement}=\text{180}°-154°=\overline{)26°}\end{array}$

Q.3

$\begin{array}{l}\mathrm{Identify}\mathrm{which}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{pairs}\mathrm{of}\mathrm{angles}\mathrm{are}\\ \mathrm{complementary}\mathrm{and}\mathrm{which}\mathrm{are}\mathrm{supplementary}.\\ \left(\mathrm{i}\right)65°,115°\left(\mathrm{ii}\right)63°,27°\left(\mathrm{iii}\right)112°,68°\\ \left(\mathrm{iv}\right)130°,50°\left(\mathrm{v}\right)45°,45°\left(\mathrm{vi}\right)80°,10°\end{array}$

Ans.

$\begin{array}{l}\left(\text{i}\right)\text{65}°,\text{115}°\\ \text{Since, the sum of complementary angle is 90}°\text{and sum of}\\ \text{supplementary angle is 180}°.\\ \text{So,}65°\text{+115}°=180°\\ \text{Therefore, given pair is supplemenatry}\text{.}\\ \left(\text{ii}\right)\text{63}°,\text{27}°\\ \text{Since, the sum of complementary angle is 90}°\text{and sum of}\\ \text{supplementary angle is 180}°.\\ \text{So,}63°\text{+27}°=90°\\ \text{Therefore, given pair is complementary}\text{.}\\ \left(\text{iii}\right)\text{112}°,\text{68}°\\ \text{Since, the sum of complementary angle is 90}°\text{and sum of}\\ \text{supplementary angle is 180}°.\\ \text{So,}112°\text{+68}°=180°\\ \text{Therefore, given pair is supplemenatry}\text{.}\\ \left(\text{iv}\right)\text{130}°,\text{50}°\\ \text{Since, the sum of complementary angle is 90}°\text{and sum of}\\ \text{supplementary angle is 180}°.\\ \text{So,}130°\text{+50}°=180°\\ \text{Therefore, given pair is supplemenatry}\text{.}\\ \left(\text{v}\right)\text{45}°,\text{45}°\\ \text{Since, the sum of complementary angle is 90}°\text{and sum of}\\ \text{supplementary angle is 180}°.\\ \text{So,}45°\text{+45}°=90°\\ \text{Therefore, given pair is complementary}\text{.}\\ \left(\text{vi}\right)\text{80}°,\text{10}°\\ \text{Since, the sum of complementary angle is 90}°\text{and sum of}\\ \text{supplementary angle is 180}°.\\ \text{So,}80°\text{+10}°=90°\\ \text{Therefore, given pair is complementary}\text{.}\end{array}$

Q.4

$\mathrm{Find}\mathrm{the}\mathrm{angle}\mathrm{which}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{its}\mathrm{complement}.$

Ans.

$\begin{array}{l}\text{Let the angle be}\mathrm{x}.\\ \text{Since, it also equal to its complement.}\\ \text{So, complement angle}=\text{}\mathrm{x}.\\ \text{Sum of complementary angle is 90}°\\ \text{So, we get}\\ \mathrm{x}+\mathrm{x}=90°\\ 2\mathrm{x}=90°\\ \mathrm{x}=\frac{90°}{2}=45°\\ \text{Thus, the angle be}\overline{)\text{45}°}.\end{array}$

Q.5

$\mathrm{Find}\mathrm{the}\mathrm{angle}\mathrm{which}\mathrm{is}\mathrm{equal}\mathrm{to}\mathrm{its}\mathrm{supplement}.$

Ans.

$\begin{array}{l}\text{Let the angle be}\mathrm{x}\text{.}\\ \text{Since, it also equal to its supplement.}\\ \text{So, supplement angle}=\text{}\mathrm{x}\text{.}\\ \text{Sum of supplementary angle is 180}°\\ \text{So, we get}\\ \mathrm{x}+\mathrm{x}=180°\\ 2\mathrm{x}=180°\\ \mathrm{x}=\frac{180°}{2}=90°\\ \text{Thus, the angle be}\overline{)\text{90}°}.\end{array}$

Q.6

$\begin{array}{l}\mathrm{In}\mathrm{the}\mathrm{given}\mathrm{figure},\angle 1\mathrm{and}\angle 2\mathrm{are}\mathrm{supplementary}\mathrm{angles}.\\ \mathrm{If}\angle 1\mathrm{is}\mathrm{decreased},\mathrm{what}\mathrm{changes}\mathrm{should}\mathrm{take}\mathrm{place}\mathrm{in}\angle 2\mathrm{so}\\ \mathrm{that}\mathrm{both}\mathrm{angles}\mathrm{still}\mathrm{remain}\mathrm{supplementary}.\end{array}$ Ans.

$\begin{array}{l}\text{Since,}\text{\hspace{0.17em}}\angle 1\text{and}\angle 2\text{\hspace{0.17em}}\text{are supplementary angles}\text{.}\\ \text{If}\angle 1\text{\hspace{0.17em}}\text{reduced, then}\angle 2\text{should be increased by the same}\\ \text{measure so that this angle remain supplementary}\text{.}\end{array}$

Q.7

$\begin{array}{l}\mathrm{Can}\mathrm{two}\mathrm{angles}\mathrm{be}\mathrm{supplementary}\mathrm{if}\mathrm{both}\mathrm{of}\mathrm{them}\mathrm{are}\\ \left(\mathrm{i}\right)\mathrm{acute}?\\ \left(\mathrm{ii}\right)\mathrm{obtuse}?\\ \left(\mathrm{iii}\right)\mathrm{right}?\end{array}$

Ans.

$\begin{array}{l}\text{(i) No, if both angles are acute, that means that both angles}\\ \text{are less than 90}°\text{. In that case, their sum can not be equal to 180}°.\\ \\ \text{(ii) No, if both angles are obtuse, that means that both angles}\\ \text{greater than 90}°.\text{In that case, their sum will exceed 180}°.\\ \\ \text{(iii) Yes, if both angles are right angles, that is, 90}°,\text{\hspace{0.17em}}\text{then their}\\ \text{sum will be exact 180}°.\end{array}$

Q.8 An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?

Ans.

$\begin{array}{l}\text{Let}\mathrm{x}\text{and}\mathrm{y}\text{be two angles having complementary angle pair}\\ \text{and}\mathrm{x}\text{is greater than 45}°.\\ \text{Then,}\\ \mathrm{x}+\mathrm{y}=90°\\ \mathrm{y}=90°-\mathrm{x}\\ \text{Thus, y will be less than 45}°.\end{array}$

Q.9

$\begin{array}{l}\mathrm{In}\mathrm{the}\mathrm{adjoining}\mathrm{figure}:\\ \left(\mathrm{i}\right)\mathrm{Is}\angle 1\mathrm{adjacent}\mathrm{to}\angle 2?\\ \left(\mathrm{ii}\right)\mathrm{Is}\angle \mathrm{AOC}\text{\hspace{0.17em}}\mathrm{adjacent}\mathrm{to}\angle \mathrm{AOE}?\\ \left(\mathrm{iii}\right)\mathrm{Do}\angle \mathrm{COE}\text{\hspace{0.17em}}\mathrm{and}\text{\hspace{0.17em}}\angle \mathrm{EOD}\text{\hspace{0.17em}}\mathrm{form}\mathrm{a}\mathrm{linear}\mathrm{pair}?\\ \left(\mathrm{iv}\right)\mathrm{Are}\angle \mathrm{BOD}\mathrm{and}\text{\hspace{0.17em}}\angle \mathrm{DOA}\text{\hspace{0.17em}}\mathrm{supplementary}?\\ \left(\mathrm{v}\right)\mathrm{Is}\angle 1\mathrm{vertically}\mathrm{opposite}\mathrm{to}\angle 4?\\ \left(\mathrm{v}\right)\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{vertically}\mathrm{opposite}\mathrm{angle}\mathrm{of}\angle 5?\end{array}$ Ans.

$\begin{array}{l}\text{(i) Yes, since they have a common vetex O and also a common}\\ \text{arm OC}\text{. Also, their non-common arms, OA}\text{​}\text{and OB are on}\\ \text{either side of the common arm}\text{.}\\ \text{(ii) No}\text{. they have a common vertex O and also a common}\\ \text{arm OA}\text{. However, their non common arms, OC and OE are on}\\ \text{the same side of the common arm}\text{. Therefore, theses are not}\\ \text{adjacent to each other}\text{.}\\ \text{(iii) Yes, since they have a common vertex O and a common}\\ \text{arm OE}\text{. Also, their non common arms OC and OD, are}\\ \text{opposite rays}\text{.}\\ \text{(iv) Yes, since}\angle \text{BOD and}\angle \text{DOA have a common vertex O and}\\ \text{their non-common arms opposite to each other}\text{.}\\ \text{(v) Yes, since these are fromed dure to the intersection of two}\\ \text{straight lines (AB and CD)}\\ \text{(vi)}\angle \text{COB is the vertically opposite angle of}\angle 5\text{as these are}\\ \text{formed due to the intersection of two straight lines AB and CD}\text{.}\end{array}$

Q.10

$\begin{array}{l}\mathrm{Indicate}\mathrm{which}\mathrm{pairs}\mathrm{of}\mathrm{angles}\mathrm{are}:\\ \left(\mathrm{i}\right)\mathrm{Vertically}\mathrm{opposite}\mathrm{angles}.\\ \left(\mathrm{ii}\right)\mathrm{Linear}\mathrm{pairs}.\end{array}$ Ans.

$\begin{array}{l}\text{(i)}\angle 1\text{,}\angle 4\text{\hspace{0.17em}}\text{and}\angle 5,\text{}\left(\angle 2+\angle 3\right)\text{are vertically opposite angles}\\ \text{as these formed due to the intersection of straight lines}\\ \text{(ii)}\angle 1\text{and}\angle \text{5,}\angle 5\text{\hspace{0.17em}}\text{and,}\angle 4\text{as these have common vertex}\\ \text{and also have non-common arms opposite to each other}\text{.}\end{array}$

Q.11 In the following figure, is

$\angle 1$

$\angle 2$

? Give reasons. Ans.

$\angle 1$

and

$\angle 2$

are not adjacent angles because they don’t have common vertex.

Q.12 Find the values of the angles x, y and z in each of the following:  Ans.

$\begin{array}{l}\text{(i) Since}\angle \mathrm{x}\text{\hspace{0.17em}and}\angle 55°\text{are vertically opposite angles.}\\ \text{So,}\mathrm{x}=\angle 55°\\ \angle \mathrm{x}°+\angle \mathrm{y}°=\angle 180°\\ \angle 55°+\angle \mathrm{y}°=\angle 180°\\ \angle \mathrm{y}°=\angle 180°-\angle 55°\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\angle 125°\\ \angle \mathrm{y}°=\angle \mathrm{z}°\left(\text{vertically\hspace{0.17em}opposite\hspace{0.17em}angles}\right)\\ \mathrm{So},\text{\hspace{0.17em}}\angle \mathrm{z}°=\angle 125°\\ \text{(ii)}\angle \mathrm{z}°=\angle 40°\left(\text{vertically\hspace{0.17em}opposite\hspace{0.17em}angles}\right)\\ \angle \mathrm{y}°+\angle \mathrm{z}°=\angle 180°\left(\text{Linear pair}\right)\\ \angle \mathrm{y}°=\angle 180°-\angle 40°\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\angle 140°\\ \angle 40°+\angle \mathrm{x}°+\angle 25°=\angle 180°\\ \angle \mathrm{x}°+\angle 65°=\angle 180°\\ \angle \mathrm{x}°=\angle 180°-\angle 65°\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\angle 115°\end{array}$

Q.13

$\begin{array}{l}\mathrm{Fill}\mathrm{in}\mathrm{the}\mathrm{blanks}:\\ \left(\mathrm{i}\right)\mathrm{If}\mathrm{two}\mathrm{angles}\mathrm{are}\mathrm{complementary},\mathrm{then}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{their}\\ \mathrm{measuresis}______.\\ \left(\mathrm{ii}\right)\mathrm{If}\mathrm{two}\mathrm{angles}\mathrm{are}\mathrm{supplementary},\mathrm{then}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{their}\\ \mathrm{measuresis}_____.\\ \left(\mathrm{iii}\right)\mathrm{Two}\mathrm{angles}\mathrm{forming}\mathrm{a}\mathrm{linear}\mathrm{pair}\mathrm{are}_______________.\\ \left(\mathrm{iv}\right)\mathrm{If}\mathrm{two}\mathrm{adjacent}\mathrm{angles}\mathrm{are}\mathrm{supplementary},\mathrm{they}\mathrm{form}\mathrm{a}__________.\\ \left(\mathrm{v}\right)\mathrm{If}\mathrm{two}\mathrm{lines}\mathrm{intersect}\mathrm{at}\mathrm{a}\mathrm{point},\mathrm{then}\mathrm{the}\mathrm{vertically}\mathrm{opposite}\\ \begin{array}{l}\mathrm{angles}\mathrm{are}\mathrm{always}_____________.\\ \begin{array}{l}\left(\mathrm{vi}\right)\mathrm{If}\mathrm{two}\mathrm{lines}\mathrm{intersect}\mathrm{at}\mathrm{a}\mathrm{point},\mathrm{and}\mathrm{if}\mathrm{one}\mathrm{pair}\mathrm{of}\\ \mathrm{vertically}\mathrm{opposite}\mathrm{angles}\mathrm{are}\mathrm{acute}\mathrm{angles},\mathrm{then}\mathrm{the}\\ \mathrm{other}\mathrm{pair}\mathrm{of}\mathrm{vertically}\mathrm{opposite}\mathrm{angles}\mathrm{are}__________.\end{array}\end{array}\end{array}$

Ans.

$\begin{array}{l}\text{Fill in the blanks}:\\ \left(\text{i}\right)\text{If two angles are complementary},\text{then the sum of their}\\ \text{measures is}\overline{)\text{90}°}.\\ \left(\text{ii}\right)\text{If two angles are supplementary},\text{then the sum of their}\\ \text{measures is}\overline{)180°}.\\ \left(\text{iii}\right)\text{Two angles forming a linear pair are}\overline{)\text{supplementary}}.\\ \left(\text{iv}\right)\text{If two adjacent angles are supplementary},\text{they}\\ \text{form a}\overline{)\text{Linear pair}}.\\ \left(\text{v}\right)\text{If two lines intersect at a point},\text{then the vertically opposite}\\ \text{angles are always}\overline{)\text{equal}}\text{​}.\\ \left(\text{vi}\right)\text{If two lines intersect at a point},\text{and if one pair of vertically}\\ \text{opposite angles are acute angles},\text{then the other pair of}\\ \text{vertically opposite angles are}\overline{)\text{obtuse angles}}.\end{array}$

Q.14

$\begin{array}{l}\mathrm{In}\mathrm{the}\mathrm{adjoining}\mathrm{figure},\mathrm{name}\mathrm{the}\mathrm{following}\mathrm{pairs}\mathrm{of}\mathrm{angle}.\\ \left(\mathrm{i}\right)\mathrm{Obtuse}\mathrm{vertically}\mathrm{opposite}\mathrm{angles}\\ \left(\mathrm{ii}\right)\mathrm{Adjacent}\mathrm{complementary}\mathrm{angles}\\ \left(\mathrm{iii}\right)\mathrm{Equal}\mathrm{supplementary}\mathrm{angles}\\ \left(\mathrm{iv}\right)\mathrm{Unequal}\mathrm{supplementary}\mathrm{angles}\\ \left(\mathrm{v}\right)\mathrm{Adjacent}\mathrm{angles}\mathrm{that}\mathrm{do}\mathrm{not}\mathrm{form}\mathrm{a}\mathrm{linear}\mathrm{pair}.\end{array}$ Ans.

$\begin{array}{l}\text{(i)}\angle \text{AOD},\text{\hspace{0.17em}}\angle \text{BOC}\\ \text{(ii)}\angle \text{EOA},\text{\hspace{0.17em}}\angle \text{AOB}\\ \text{(iii)}\text{\hspace{0.17em}}\angle \text{EOB},\text{\hspace{0.17em}}\angle \text{EOD}\\ \text{(iv)}\text{\hspace{0.17em}}\angle \text{EOA},\text{\hspace{0.17em}}\angle \text{EOC}\\ \text{(v)}\text{\hspace{0.17em}}\angle \text{AOB}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle \text{AOE},\text{\hspace{0.17em}}\angle \text{AOE}\text{\hspace{0.17em} and}\text{\hspace{0.17em}}\angle \text{EOD},\text{\hspace{0.17em}}\angle \text{EOD}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle \text{COD}\text{.}\end{array}$

Q.15

$\begin{array}{l}\mathrm{State}\mathrm{the}\mathrm{property}\mathrm{that}\mathrm{isused}\mathrm{in}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{statements}?\\ \begin{array}{l}\left(\mathrm{i}\right)\mathrm{If}\mathrm{a}\parallel \mathrm{b},\mathrm{then}\angle 1=\angle 5.\\ \left(\mathrm{ii}\right)\mathrm{If}\angle 4=\angle 6,\mathrm{then}\mathrm{a}\parallel \mathrm{b}.\\ \left(\mathrm{iii}\right)\mathrm{If}\angle 4+\angle 5=180°,\mathrm{then}\mathrm{a}\parallel \mathrm{b}.\end{array}\end{array}$ Ans.

$\begin{array}{l}\text{(i) Corresponding angles property}\\ \text{(ii) Alternate interior angles property}\\ \text{(ii) Interior angles on the same side of transversal are supplementary.}\end{array}$

Q.16 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. Ans.

$\begin{array}{l}\text{(i)}\angle 1\text{and}\angle 5\text{,}\angle 2\text{and}\angle 6\text{,}\angle 3\text{and}\angle 7,\text{}\angle 4\text{and}\angle 8.\\ \text{(ii)}\angle 2\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\angle 8,\text{\hspace{0.17em}}\angle 3\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle 5\\ \left(\text{iii)}\angle 2\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle 5,\text{\hspace{0.17em}}\angle 3\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle 8\\ \text{(iv)}\angle 1\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle 3,\text{\hspace{0.17em}}\angle 2\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle 4,\text{\hspace{0.17em}}\angle 5\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle 7,\text{\hspace{0.17em}}\angle 6\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\angle 8.\end{array}$

Q.17

$\mathrm{In}\mathrm{the}\mathrm{adjoining}\mathrm{figure},\mathrm{p}\parallel \mathrm{q}.\mathrm{Find}\mathrm{the}\mathrm{unknown}\mathrm{angles}.$ Ans.

$\begin{array}{l}\angle \mathrm{d}=125°\left(\text{Corresponding\hspace{0.17em}angles}\right)\\ \angle \mathrm{e}=180°125°=55°\left(\text{Linear\hspace{0.17em}pair}\right)\\ \angle \mathrm{f}=\angle \mathrm{e}=55°\left(\text{Vertically\hspace{0.17em}opposite\hspace{0.17em}angles}\right)\\ \angle \mathrm{c}=\angle \mathrm{f}=55°\left(\text{Corresponding\hspace{0.17em}angles}\right)\\ \angle \mathrm{a}=\angle \mathrm{e}=55°\left(\text{Corresponding\hspace{0.17em}angles}\right)\\ \angle \mathrm{b}=\angle \mathrm{d}=125°\left(\text{Vertically\hspace{0.17em}opposite\hspace{0.17em}angles}\right)\end{array}$

Q.18 Find the value of x in each of the following figures if

$\mathrm{l}\parallel \mathrm{m}$

. Ans.

$\begin{array}{l}\text{(i)}\\ \angle \mathrm{y}=110°\text{(corresponding angles)}\\ \angle \mathrm{x}+\angle \mathrm{y}=180°\left(\text{linear pair}\right)\\ \mathrm{So},\text{\hspace{0.17em}}\angle \mathrm{x}=180°-110°=70°\\ \\ \text{(ii)}\\ \angle \mathrm{x}=100°\left(\text{corresponding\hspace{0.17em}angles}\right)\end{array}$

Q.19

$\mathrm{In}\mathrm{the}\mathrm{given}\mathrm{figure},\mathrm{the}\mathrm{arms}\mathrm{of}\mathrm{two}\mathrm{angles}\mathrm{are}\mathrm{parallel}.\phantom{\rule{0ex}{0ex}}\mathrm{If}\angle \mathrm{ABC}=70°,\mathrm{then}\mathrm{find}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{i}\right)\angle \mathrm{DGC}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(\mathrm{ii}\right)\angle \mathrm{DEF}$ Ans.

$\begin{array}{l}\text{(i) Consdier that AB}\parallel \text{DG and a transerval line BC is}\\ \text{intersecting them.}\\ \angle \mathrm{DGC}=\angle \mathrm{ABC}\text{}\left(\text{Corresponding angles}\right)\\ \mathrm{SO},\overline{)\angle \mathrm{DGC}=70°}\\ \\ \text{(ii) Consdier that BC}\parallel \text{EF and a transerval line DE is}\\ \text{intersecting them.}\\ \angle \mathrm{DEF}=\angle \mathrm{DGC}\text{}\left(\text{Corresponding angles}\right)\\ \overline{)\angle \mathrm{DEF}=70°}\end{array}$

Q.20 In the given figures below, decide whether l is parallel to m. Ans.

$\begin{array}{l}\text{(i)}\\ \text{Consider two lines, l and m, and a transversal line n which is}\\ \text{intersecting them. Sum of the interior angles on the same side}\\ \text{of transersal}=126°+44°=170°\text{.}\\ \text{As the sum of interior angles on the same side of transervsal is}\\ \text{not 180}°\text{, Therefore}\mathrm{l}\text{is not parallel to}\mathrm{m}\text{.}\\ \\ \text{(ii)}\mathrm{x}+75°=180°\text{(linear pair)}\\ \mathrm{x}=180°-75°=105°\\ \mathrm{For}\text{}\mathrm{l}\text{and}\mathrm{m}\text{to be parallel to each other, corresponding}\\ \text{angles (}\angle \text{ABC and}\angle \mathrm{x}\right)\text{\hspace{0.17em}should be equal. However, here they}\\ \text{are 75}°\text{and 105}°\text{.}\\ \begin{array}{l}\text{Hence these lines are not parallel to each other.}\\ \\ \text{(iii)}\mathrm{x}+123°=180°\\ \mathrm{x}=\text{180}°-123°=57°\\ \mathrm{For}\text{l and m to be parallel to each other, corresponding}\\ \text{angles (}\angle \text{ABC and}\angle \mathrm{x}\right)\text{\hspace{0.17em}should be equal. However, here they}\\ \text{are 57}°\text{and 57}°\text{.}\\ \text{Hence these lines are parallel to each other.}\\ \\ \text{(iv) 98}°+\mathrm{x}=180°\\ \mathrm{x}=180°-98°=82°\\ \text{For}\mathrm{l}\text{and}\mathrm{m}\text{to be parallel to each other, corresponding}\\ \text{angles (}\angle \text{ABC and}\angle \mathrm{x}\right)\text{\hspace{0.17em}should be equal. However, here they}\\ \text{are 72}°\text{and 82}°\text{.}\\ \text{Hence these lines are not parallel to each other}\end{array}\end{array}$

## 1. How are the NCERT Solutions for Class 7 Mathematics Chapter 5 useful for students?

NCERT Solutions for Class 7 Mathematics Chapter 5 are the best study materials for students to solve and practise the NCERT textbook questions. These answers are written in a detailed and structured format, making it easy for students who find the  text-end questions difficult to answer. These solutions are  highly beneficial and  students will know  how to  frame  answers in the final exams.

## 2. Where can I find quality NCERT Solutions for Class 7 Mathematics Chapter 5 Lines and Angles?

Extramarks offers quality NCERT Solutions for Class 7 Mathematics Chapter 5 that students can rely on for their exam preparations. These answers are solved by subject matter experts who provide stepwise explanations for problems. Furthermore, students can easily access these materials from Extramarks.

## 3. How many questions are there in NCERT Solutions Class 7 Mathematics Chapter 5 Lines and Angles?

There are two exercises in Class 7 Mathematics Chapter 5 Lines and Angles. Exercise 5.1 has 14 questions with most of its questions having subparts. Exercise 5.2 has six questions with its questions having sub-parts too. These questions are based on the topics covered in the chapter Lines and Angles and require a thorough understanding of the chapter to master the topic.

## 4. What are the important topics covered in NCERT Solutions Class 7 Mathematics Chapter 5?

The most important topics covered in NCERT Solutions for Class 7 Mathematics Chapter 5 are Relative Angles and their properties, Complementary Angles, Supplementary Angles, Adjacent Angles, Linear Pairs, Vertically Opposite Angles, Pairs of Lines, Intersecting Lines, Transversal, the Angle made by a Transversal, a Transversal of Parallel lines, and Checking for Parallel Lines.

## 5. How to score full marks in Class 7 Mathematics Chapter 5?

To score full marks in any domain of Mathematics, you must practise, practise, and practise . Regular practise  and conceptual clarity are not only key to understanding all concepts on a deeper level but they also help in avoiding silly mistakes. The questions given at the end of the chapter help students to practise the concepts they have learnt in the chapter. For this, they may use NCERT Solutions for Class 7 Mathematics Chapter 5 to extensively practise these answers. You will also get to know how to solve those tricky questions and you will be able to solve them without much difficulty.