# NCERT Solutions and Notes for Class 7 Maths Chapter 5: Lines and Angles (Free PDF)

In NCERT Class 7 Maths Chapter 5, Lines and Angles, we will study the concept of different angles, their properties, and how to draw them along with the relation between the two. Students will also learn to draw these angles and derive useful relations between them. Let us now have a look at the NCERT Class 7 Maths Chapter 5 Lines and Angles Notes and Solutions (PDF).

## NCERT Class 7 Maths Chapter 5 Notes – PDF Available

Check the topic-wise notes for NCERT Maths Class 7 – Chapter 5 below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the e𝑥am hall.

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Let us see some related angles below.

1. Complementary Angles: When the sum of the measures of two angles is 90°, the angles are called complementary angles.

Note:- Whenever two angles are complementary, each angle is said to be the complement of the other angle.

For example, two complementary angles are shown below.

1. Supplementary Angles: When the sum of the measures of two angles is 180°, the angles are called complementary angles.

Note:- Whenever two angles are supplementary, each angle is said to be the supplement of the other angle.

For example, two supplementary angles are shown below.

1. Adjacent Angles: Adjacent angles have a common vertex with one common arm and the non-common arms of these angles are on either side of the common arm.

An example of adjacent angles is given below.

1. Linear Pair: A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.

An example of the linear pair is given below.

1. Vertically Opposite Angles: When two lines intersect, they form angles that are equal in measure. These angles are called the vertically opposite angles. The example of vertically opposite angles is shown below.

In the above diagram, angles 1 and 3 are vertically opposite angles.

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### Topic 2: Pair of Lines

A few concepts related to the pair of lines are given below.

1. Intersecting Lines: Two lines l and m intersect if they have a point in common. This common point O is their point of intersection. Two intersecting lines “l” and “m” are shown in the figure below.
1. Transversal: A line that intersects two or more lines at distinct points is called a transversal. In the diagram shown below, the line “p” is a transversal that intersects the lines “l” and “m”.
1. Transversal of Parallel Lines: The results of the transversal of the parallel lines are given below.
• If two parallel lines are cut by a transversal, each pair of corresponding angles is equal in measure.
• If two parallel lines are cut by a transversal, each pair of alternate interior angles is equal.
• If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal is supplementary.

The above results are illustrated in the diagram below.

From the above diagram, we can say that:

• Each pair of corresponding angles are equal, i.e. ∠1 = ∠5, ∠3 = ∠7, ∠2 = ∠6, ∠4 = ∠8.
• Each pair of alternate interior angles is equal, i.e. ∠3 = ∠6, ∠4 = ∠5
• Each pair of interior angles on the same side of the transversal are supplementary, i.e. ∠3 + ∠5 = 180°, ∠4 + ∠6 = 180°

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## NCERT Solutions of Class 7 Maths Chapter 5: Lines and Angles – Free PDF Download

Below we have provided solutions for NCERT Class 7 Maths Chapter 5, Lines and Angles. Go through for answers to some important questions.

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### E𝑥ercise 5.1 Solutions

Q 1. Find the complement of each of the following angles:

Solutions. We know that the sum of the measures of two complementary angles is 90°. So, the complement of each given angle is calculated below.

1. The measures of the given angle = 20°

Let us assume the measure of the unknown angle to be 𝑥.

∴ 𝑥 + 20° = 90° ⇒ 𝑥 = 70°

1. The measures of the given angle = 63°

Let us assume the measure of the unknown angle to be 𝑥.

∴ 𝑥 + 63° = 90° ⇒ 𝑥 = 27°

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Q 2. An angle is greater than 45º. Is its complementary angle greater than 45º or equal to 45º or less than 45º?

Solutions. The sum of the measures of two complementary angles is 90°. So, for an angle greater than 45°, its complementary angle must be less than 45°.

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Q 3. In the adjoining figure:

1. Is ∠1 adjacent to ∠2?
2. Is ∠AOC adjacent to ∠AOE?
3. Do ∠COE and ∠EOD form a linear pair?
4. Are ∠BOD and ∠DOA supplementary?
5. Is ∠1 vertically opposite to ∠4?
6. What is the vertically opposite angle of ∠5?

Solutions. The answers are given below.

1. Yes, ∠1 is adjacent to ∠2 as both of these angles have a common vertex “O”, a common arm OC and both the uncommon arms are on either side of the common arm.
2. No, ∠AOC is not adjacent to ∠AOE. This is because despite sharing a common vertex “O” and a common arm “OA”, the uncommon arms of both these angles are not on either side of the common arm.
3. Yes, ∠COE and ∠EOD form a linear pair. This is because the uncommon arms OC and OD are opposite rays.
4. Yes, ∠BOD and ∠DOA are supplementary. This is because both of these angles have a common vertex “O”, a common arm “OD” and the uncommon arms are opposite to each other.
5. Yes, ∠1 is vertically opposite to ∠4 because both these angles are formed by the intersection of lines AB and CD.
6. ∠BOC is vertically opposite to ∠5.

### E𝑥ercise 5.2 Solutions

Q 1. State the property that is used in each of the following statements.

1. If a || b, then ∠1 = ∠5.
2. If ∠4 = ∠6, then a || b.
3. If ∠4 + ∠5 = 180°, then a || b.

Solutions. The answers are given below.

1. Corresponding angles
2. Alternate interior angles
3. Each pair of interior angles on the same side of the transversal are supplementary.

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## FAQs

Q.1. What are complementary angles?

Ans: When the sum of the measures of two angles is 90°, the angles are called complementary angles.

Q.2. What are supplementary angles?

Ans: When the sum of the measures of two angles is 180°, the angles are called complementary angles.

Q.3. What is a transversal?

Ans: A line that intersects two or more lines at distinct points is called a transversal.

This was all about NCERT Class 7 Maths Chapter 5, Lines and Angles in which we studied different angles and their properties. We also studied the properties of angles in relation to each other. Download the NCERT Class 7 Maths Chapter 5 Notes and Solutions PDF to ace your e𝑥am preparations. Follow the CBSE Class 7 Maths Solutions and Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 7 Maths.