NCERT Solutions for Class 7 Maths Exercise 5.1 Chapter 5 Lines and Angles

NCERT Solutions for Class 7 Maths Exercise 5.1 Chapter 5 Lines and Angles are given here in simple PDF. This exercise of NCERT Solutions for Class 7 Maths Chapter 5 has topics related to complementary angles, supplementary angles, adjacent angles, linear pairs and vertically opposite angles. When the sum of two angles is 90 degrees, such angles are complementary angles. When the sum of two angles is 180 degrees, such angles are supplementary angles. When the angles have a common vertex and a common arm but no common interior points, such angles are adjacent angles. Learn more about these topics by solving the questions of NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles with the help of solutions provided here.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles – Exercise 5.1

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Access Answers to NCERT Solutions Class 7 Maths Chapter 5 – Lines and Angles Exercise 5.1

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

(i)

Solution:-

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

The given angle is 20^o

Let the measure of its complement be x^o.

Then,

= x + 20^o = 90^o

= x = 90^o – 20^o

= x = 70^o

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

(ii)

Solution:-

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

The given angle is 63^o

Let the measure of its complement be x^o.

Then,

= x + 63^o = 90^o

= x = 90^o – 63^o

= x = 27^o

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

(iii)

Solution:-

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

The given angle is 57^o

Let the measure of its complement be x^o.

Then,

= x + 57^o = 90^o

= x = 90^o – 57^o

= x = 33^o

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

2. Find the supplement of each of the following angles:

(i)

Solution:-

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

The given angle is 105^o

Let the measure of its supplement be x^o.

Then,

= x + 105^o = 180^o

= x = 180^o – 105^o

= x = 75^o

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

(ii)

Solution:-

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

The given angle is 87^o

Let the measure of its supplement be x^o.

Then,

= x + 87^o = 180^o

= x = 180^o – 87^o

= x = 93^o

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

(iii)

Solution:-

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

The given angle is 154^o

Let the measure of its supplement be x^o.

Then,

= x + 154^o = 180^o

= x = 180^o – 154^o

= x = 26^o

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

3. Identify which of the following pairs of angles are complementary and which are supplementary.

(i) 65^o, 115^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 65^o + 115^o

= 180^o

If the sum of two angles measures 180^o, then the two angles are said to be supplementary.

∴ These angles are supplementary angles.

(ii) 63^o, 27^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 63^o + 27^o

= 90^o

If the sum of two angle measures is 90^o, then the two angles are said to be complementary.

∴ These angles are complementary angles.

(iii) 112^o, 68^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 112^o + 68^o

= 180^o

If the sum of two angle measures is 180^o, then the two angles are said to be supplementary.

∴ These angles are supplementary angles.

(iv) 130^o, 50^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 130^o + 50^o

= 180^o

If the sum of two angle measures is 180^o, then the two angles are said to be supplementary.

∴ These angles are supplementary angles.

(v) 45^o, 45^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 45^o + 45^o

= 90^o

If the sum of two angle measures is 90^o, then the two angles are said to be complementary.

∴ These angles are complementary angles.

(vi) 80^o, 10^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 80^o + 10^o

= 90^o

If the sum of two angle measures is 90^o, then the two angles are said to be complementary.

∴ These angles are complementary angles.

4. Find the angle which is equal to its complement.

Solution:-

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

We know that sum of measures of complementary angle pair is 90^o.

Then,

= x + x = 90^o

= 2x = 90^o

= x = 90/2

= x = 45^o

Hence, the angle which is equal to its complement is 45^o.

5. Find the angle which is equal to its supplement.

Solution:-

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

We know that sum of measures of supplementary angle pair is 180^o.

Then,

= x + x = 180^o

= 2x = 180^o

= x = 180/2

= x = 90^o

Hence, the angle which is equal to its supplement is 90^o.

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 angles still remain supplementary?

Solution:-

From the question, 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.

7. Can two angles be supplementary if both of them are:

(i). Acute?

Solution:-

No. If two angles are acute, which means less than 90^o, the two angles cannot be supplementary because their sum will always be less than 90^o.

(ii). Obtuse?

Solution:-

No. If two angles are obtuse, which means more than 90^o, then two angles cannot be supplementary because their sum will always be more than 180^o.

(iii). Right?

Solution:-

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

∴90^o + 90^o = 180

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?

Solution:-

Let us assume the complementary angles be p and q,

We know that sum of measures of complementary angle pair is 90^o.

Then,

= p + q = 90^o

It is given in the question that p > 45^o

Adding q on both sides,

= p + q > 45^o + q

= 90^o > 45^o + q

= 90^o – 45^o > q

= q < 45^o

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

9. In the adjoining figure:

(i) Is ∠1 adjacent to ∠2?

Solution:-

By observing the figure, we came to conclude that,

Yes, as ∠1 and ∠2 have a common vertex, i.e. O and a common arm OC.

Their non-common arms, OA and OE, are on both sides of the common arm.

(ii) Is ∠AOC adjacent to ∠AOE?

Solution:-

By observing the figure, we came to conclude that,

No, since they have a common vertex O and common arm OA.

But they have no non-common arms on both sides of the common arm.

(iii) Do ∠COE and ∠EOD form a linear pair?

Solution:-

By observing the figure, we came to conclude that,

Yes, as ∠COE and ∠EOD have a common vertex, i.e. O and a common arm OE.

Their non-common arms, OC and OD, are on both sides of the common arm.

(iv) Are ∠BOD and ∠DOA supplementary?

Solution:-

By observing the figure, we came to conclude that,

Yes, as ∠BOD and ∠DOA have a common vertex, i.e. O and a common arm OE.

Their non-common arms, OA and OB, are opposite to each other.

(v) Is ∠1 vertically opposite to ∠4?

Solution:-

Yes, ∠1 and ∠2 are formed by the intersection of two straight lines AB and CD.

(vi) What is the vertically opposite angle of ∠5?

Solution:-

∠COB is the vertically opposite angle of ∠5 because these two angles are formed by the intersection of two straight lines AB and CD.

10. Indicate which pairs of angles are:

(i) Vertically opposite angles.

Solution:-

By observing the figure, we can say that,

∠1 and ∠4, ∠5 and ∠2 + ∠3 are vertically opposite angles because these two angles are formed by the intersection of two straight lines.

(ii) Linear pairs.

Solution:-

By observing the figure, we can say that,

∠1 and ∠5, ∠5 and ∠4, as these have a common vertex and also have non-common arms opposite to each other.

11. In the following figure, is ∠1 adjacent to ∠2? Give reasons.

Solution:-

∠1 and ∠2 are not adjacent angles because they are not lying on the same vertex.

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

(i)

Solution:-

∠x = 55^o, because vertically opposite angles.

∠x + ∠y = 180^o … [∵ linear pair]

= 55^o + ∠y = 180^o

= ∠y = 180^o – 55^o

= ∠y = 125^o

Then, ∠y = ∠z … [∵ vertically opposite angles]

∴ ∠z = 125^o

(ii)

Solution:-

∠z = 40^o, because vertically opposite angles.

∠y + ∠z = 180^o … [∵ linear pair]

= ∠y + 40^o = 180^o

= ∠y = 180^o – 40^o

= ∠y = 140^o

Then, 40 + ∠x + 25 = 180^o … [∵angles on straight line]

65 + ∠x = 180^o

∠x = 180^o – 65

∴ ∠x = 115^o

13. Fill in the blanks:

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

Solution:-

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 ______.

Solution:-

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

(iii) Two angles forming a linear pair are _______________.

Solution:-

Two angles forming a linear pair are supplementary.

(iv) If two adjacent angles are supplementary, they form a ___________.

Solution:-

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

(v) If two lines intersect at a point, then the vertically opposite angles are always

_____________.

Solution:-

If two lines intersect at a point, then the vertically opposite angles are always equal.

(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 __________.

Solution:-

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 obtuse angles.

14. In the adjoining figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles

Solution:-

∠AOD and ∠BOC are obtuse vertically opposite angles in the given figure.

(ii) Adjacent complementary angles

Solution:-

∠EOA and ∠AOB are adjacent complementary angles in the given figure.

(iii) Equal supplementary angles

Solution:-

∠EOB and EOD are the equal supplementary angles in the given figure.

(iv) Unequal supplementary angles

Solution:-

∠EOA and ∠EOC are the unequal supplementary angles in the given figure.

(v) Adjacent angles that do not form a linear pair

Solution:-

∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD are the adjacent angles that do not form a linear pair in the given figure.

Access Other Exercise of NCERT Solutions for Class 7 Maths Chapter 5 – Lines and Angles

Exercise 5.2 Solutions

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NCERT Solutions for Class 7 Maths

NCERT Solutions for Class 7 

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