NCERT Class 7 Maths Chapter 5 ‘Lines and Angles’ Exercise 5.1

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Welcome to Online Tutorial Classes! We are excited to present a valuable resource for CBSE students studying Class 7 Mathematics. In this post, we will delve into the NCERT class 7 Maths chapter 5 ‘Lines and Angles’ exercise 5.1 from the CBSE curriculum and provide you with a comprehensive notes and worksheets to help you master this important topic.

NCERT Class 7 Maths Chapter 5, ‘Lines and Angles’, exercise 5.1 introduces students to the concepts of angles, their relationships, and the properties of lines and angles formed by intersecting and parallel lines.

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NCERT class 7 Maths Chapter 5 ‘Lines and Angles’ Exercise 5.1 Overview

Chapter 5 of CBSE Class 7 Maths, “Lines and Angles,” exercise 5.1 plunges into the fundamental building blocks of geometry. It starts by defining points, lines, and line segments before venturing into the world of angles. You’ll encounter different types of angles like acute, obtuse, and right angles, learning their relationships with each other through concepts like complementary, supplementary, and vertically opposite angles.

The chapter then explores how lines interact, introducing parallel lines and transversals, and delving into the fascinating relationships between the angles they create. By the end, you’ll be able to recognize and measure angles, navigate the intricacies of intersecting and parallel lines, and even discover the secret sum of angles inside a triangle! It’s a foundational journey into the world of shapes and their interactions, paving the way for future explorations in geometry.

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NCERT class 7 Maths Chapter 5 ‘Lines and Angles’ Exercise 5.1

Question 1

Find the complement of each of the following angles:

Solution:

(i) Two angles are said to be complementary if the sum of their measures is 90^o.

The given angle is 20^o

Therefore, the complement angle will be = (90-20)^o. = 70^o

Hence, the complement of the given angle measures 70^o.

(ii)

Two angles are said to be complementary if the sum of their measures is 90^o.

The given angle is 63^o

Therefore, the complement angle will be = (90-63)^o. = 27^o

Hence, the complement of the given angle measures 27^o.

(iii)

Two angles are said to be complementary if the sum of their measures is 90^o.

The given angle is 57^o

Therefore, the complement angle will be = (90-57)^o. = 330^o

Hence, the complement of the given angle measures 33^o.

Question 2

Find the supplement of each of the following angles:

Solution:

(i) Two angles are said to be supplementary if the sum of their measures is 180^o.

The given angle is 105^o

Therefore, the supplement angle will be = (180-105)^o. = 75^o

Hence, the complement of the given angle measures 75^o.

(ii) Two angles are said to be supplementary if the sum of their measures is 180^o.

The given angle is 87^o

Therefore, the supplement angle will be = (180-87)^o. = 93^o

Hence, the complement of the given angle measures 93^o.

(iii) Two angles are said to be supplementary if the sum of their measures is 180^o.

The given angle is 154^o

Therefore, the supplement angle will be = (180-154)^o. = 26^o

Hence, the complement of the given angle measures 26^o.

Question 3

Identify which of the following pairs of angles are complementary and which are supplementary.
(i) 65º, 115º (ii) 63º, 27º (iii) 112º, 68º (iv) 130º, 50º (v) 45º, 45º (vi) 80º, 10º

Solution:

(i) 65^o, 115^o

Solution:-

If the sum of the two angles is 180^o they are called supplementary angles and If the sum of the two angles is 90^o they are called complementary angles.

Sum of the given angles is = 65^o + 115^o

= 180^o

∴ These angles are supplementary angles.

(ii) 63^o, 27^o

Solution:-

If the sum of the two angles is 180^o they are called supplementary angles and If the sum of the two angles is 90^o they are called complementary angles.

Sum of the given angles is = 63^o + 27^o

= 90^o

∴ The angles are complementary angles.

(iii) 112^o, 68^o

Solution:-

If the sum of the two angles is 180^o they are called supplementary angles and If the sum of the two angles is 90^o they are called complementary angles.

Sum of the given angles is = 112^o + 68^o

= 180^o

∴ These angles are supplementary angles.

(iv) 130^o, 50^o

Solution:-

If the sum of the two angles is 180^o they are called supplementary angles and If the sum of the two angles is 90^o they are called complementary angles.

Sum of the given angles is = 130^o + 50^o

= 180^o

∴ These angles are supplementary angles.

(v) 45^o, 45^o

Solution:-

If the sum of the two angles is 180^o they are called supplementary angles and If the sum of the two angles is 90^o they are called complementary angles.

Sum of the given angles is = 45^o + 45^o

= 90^o

∴ These angles are complementary angles.

(vi) 80^o, 10^o

Solution:-

If the sum of the two angles is 180^o they are called supplementary angles and If the sum of the two angles is 90^o they are called complementary angles.

Sum of the given angles is = 80^o + 10^o

= 90^o

∴ These angles are complementary angles.

Question 4

Find the angle which is equal to its complement.

Solution:

Let the measure of the required angle be x^o.

We know that the sum of the complementary angles is 90^o.

Then,

∴ x + x = 90^o

Or 2x = 90^o

Or x = 90/2

Or x = 45^o

Hence, the required angle measure is 45^o.

Question 5

Find the angle which is equal to its supplement.

Solution:

Let the measure of the required angle be x^o.

We know that the sum of the supplementary angles is 180^o.

∴ x + x = 180^o

Or 2x = 180^o

Or x = 180/2

Or x = 90^o

Hence, the required angle measure is 90^o.

Question 6

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

Solution:

It is given that:

∠1 and ∠2 are supplementary angles.

If ∠1 is decreased, then ∠2 must be increased by the same value. Hence, this angle pair remains supplementary.

Question 7

Can two angles be supplementary if both of them are:
(i) acute? (ii) obtuse? (iii) right?

Solution:

(i). Acute?

If two angles are acute, ie less than 90^o, then they cannot be supplementary because their sum will always be less than 180^o.

(ii). Obtuse?

If two angles are obtuse, which means greater than 90^o, then they cannot be supplementary because their sum will always be more than 180^o.

(iii). Right?

If two angles are right, which means both measure 90^o, then they can form a supplementary pair.

∴ 90^o + 90^o = 180

Question 8

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

Solution:

We know that the sum of two complementary angles is 90^o.

If one of the angles is greater than 45^o then the second angle has to be less than 45^o

Therefore, its complementary angle is less than 45^o.

Question 9

Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is __________.
(ii) If two angles are supplementary, then the sum of their measures is __________. (iii) If two adjacent angles are supplementary, they form a ____.

Solution:

(i) If two angles are complementary, then the sum of their measures is 90^o.

(ii) If two angles are supplementary, then the sum of their measures is 180^o .

(iii) If two adjacent angles are supplementary, they form a linear pair.

Question 10

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

Solution:

(i) ∠AOD and BOC are obtuse vertically opposite angles.

(ii) ∠BOA and ∠AOE are adjacent complementary angles.

(iii) ∠BOE and ∠EOD are equal supplementary angles.

(iv) ∠BOA and ∠AOD; ∠COD and ∠DOA are unequal supplementary angles

(v) ∠BOA and ∠AOE; ∠AOE and ∠EOD; ∠EOD and ∠DOC do not form linear pair.

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CBSE class 7 Mathematics Notes

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