NCERT Solutions Class 7th Math 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 26^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 angle measures is 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 angles 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 required angle measures is 45^o.

5. Find the angles 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 required angle measures 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, means less than 90^o, the two angles cannot be supplementary. Because, their sum will be always less than 90^o.

(ii). Obtuse?

Solution: No. If two angles are obtuse, means more than 90^o, the two angles cannot be supplementary. Because, their sum will be always more than 180^o.

(iii). Right?

Solution: Yes. If two angles are right, means both measures 90^o, then two angles can form a supplementary pair.
∴90^o + 90^o = 180^o.

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

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

10. 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.