NCERT Solutions Class 7 Maths Chapter 5 Lines and Angles Ex 5.1

NCERT Solutions Class 7 Mathematics 
Chapter – 5 (Lines and Angles)

The NCERT Solutions in English Language for Class 7 Mathematics Chapter – 5 Lines and Angles Exercise 5.1 has been provided here to help the students in solving the questions from this exercise. 

Chapter : 5 Lines and Angles

• NCERT Solution Class 7 Maths Exercise – 5.2

Exercise – 5.1 

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

(i) (ii) (iii)

Solution –
(i) 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.
⇒ x + 20^o = 90^o
⇒ x = 90^o – 20^o
⇒ x = 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
Let the measure of its complement be x^o.
⇒ x + 63^o = 90^o
⇒ x = 90^o – 63^o
⇒ x = 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
Let the measure of its complement be x^o.
⇒ 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) (ii) (iii)

Solution –
(i) 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.
⇒ x + 105^o = 180^o
⇒ x = 180^o – 105^o
⇒ x = 75^o
Hence, the supplement 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
Let the measure of its supplement be x^o.
⇒ x + 87^o = 180^o
⇒ x = 180^o – 87^o
⇒ x = 93^o
Hence, the supplement 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
Let the measure of its supplement be x^o.
⇒ 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
(ii) 63°, 27°
(iii) 112°, 68°
(iv) 130°, 50°
(v) 45°, 45°

Solution –
(i) 65^o, 115^o
65° (+) 115° = 180°
∴ These angles are supplementary angles.

(ii) 63^o, 27^o
63° (+) 27° = 90°
∴ These angles are complementary angles.

(iii) 112^o, 68^o
112° (+) 68° = 180°
∴ These angles are supplementary angles.

(iv) 130^o, 50^o
130° (+) 50° = 180°
∴ These angles are supplementary angles.

(v) 45^o, 45^o
45° (+) 45° = 90°
∴ These angles are complementary angles.

(vi) 80^o, 10^o
80° (+) 10° = 90°
∴ These angles are complementary angles.

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

Solution –
Let the required angle be x°.
We know that, sum of measures of complementary angle pair is 90^o.
⇒ x + x = 90^o
⇒ 2x = 90^o
⇒ x =
⇒ 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.
⇒ x + x = 180^o
⇒ 2x = 180^o
⇒ x =
⇒ 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?
(ii) Obtuse?
(iii) Right?

Solution –
(i) Acute?
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?
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?
Yes. If two angles are right, means both measures 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 x and y,
We know that, sum of measures of complementary angle pair is 90^o.
Then,
⇒ x + y = 90^o
It is given in the question that p > 45^o
Adding q on both the sides,
⇒ x + y > 45^o + y
⇒ 90^o > 45^o + y
⇒ 90^o – 45^o > y
⇒ y < 45^o
Hence, its complementary angle is less than 45^o.

9. In the adjoining figure:

(i) Is ∠1 adjacent to ∠2?
(ii) Is ∠AOC adjacent to∠AOE?
(iii) Do ∠COE and ∠EOD form a linear pair?
(iv) Are ∠BOD and ∠DOA supplementary?
(v) Is ∠1 vertically opposite angle to ∠4?
(vi) What is the vertically opposite angle of ∠5?

Solution –
(i) Is ∠1 adjacent to ∠2?
Yes, ∠1 and ∠2 are adjacent angles.

(ii) Is ∠AOC adjacent to ∠AOE?
No, ∠AOC is not adjacent to ∠AOE. [ ∵  OC and OE do not lie on either side of common arm OA] .

(iii) Do ∠COE and ∠EOD form a linear pair?
Yes, ∠COE and ∠EOD form a linear pair of angles.

(iv) Are ∠BOD and ∠DOA supplementary?
Yes, ∠BOD and ∠DOA are supplementary. [∵ ∠BOD + ∠DOA = 180°]

(v) Is ∠1 vertically opposite to ∠4?
Yes, ∠1 is vertically opposite to ∠4.

(vi) What is the vertically opposite angle of ∠5?
Vertically opposite angle of ∠5 is ∠2 + ∠3 i.e. ∠BOC.

10. Indicate which pairs of angles are:
(i) Vertically opposite angles.
(ii) Linear pairs.

Solution –
(i) Vertically opposite angles.
Vertically opposite angles are ∠1 and ∠4, ∠5 and (∠2 + ∠3)

(ii) Linear pairs.
∠1 and ∠5, ∠5 and ∠4

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

Solution –
∠1 and ∠2 are not adjacent angles. Because, they are not lie on the same vertex.

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

Solution –
(i)
∠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)
∠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 ________.
(ii) If two angles are supplementary, then the sum of their measures is ________.
(iii) Two angles forming a linear pair are ________.
(iv) If two adjacent angles are supplementary, they form a ________.
(v) If two lines intersect at a point, then the vertically opposite angles are always ________.
(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 –
(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) Two angles forming a linear pair are Supplementary.
(iv) 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 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 Obtuse angle.

14. 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 but do not form a linear pair.

Solution –
(i) Obtuse vertically opposite angles
∠AOD and ∠BOC are obtuse vertically opposite angles in the given figure.

(ii) Adjacent complementary angles
∠EOA and ∠AOB are adjacent complementary angles in the given figure.

(iii) Equal supplementary angles
∠EOB and EOD are the equal supplementary angles in the given figure.

(iv) Unequal supplementary angles
∠EOA and ∠EOC are the unequal supplementary angles in the given figure.

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