Class 7 Maths Chapter 6 Question Answers - Lines and Angles

Q1. Write the complementary angle of 57^∘.
Ans: The sum of complementary angles is 180^∘.
Let the other angle be x, then
x + 57^∘ = 90^∘
x = 90^∘ − 57^∘
x = 33^∘

Q2. Write the supplementary angle of 103^∘.
Ans: The sum of complementary angles is 180^∘.
Let the other angle be x, then
x + 103^∘ = 180^∘
x = 180^∘− 103^∘
x = 77^∘

Q3. Identify the supplementary and complementary angles.
(a) 60^∘, 120^∘
(b) 30^∘, 60^∘
(c) 35^∘, 145∘
(d) 12^∘, 78^∘
Ans: Pair of angles whose sum is 180^∘ are called supplementary angles.
Here,
60^∘, 120^∘ and 35^∘, 145^∘ are supplementary angles.
Pair of angles whose sum is 90^∘ are called complementary angles.
Here, 30^∘, 60^∘ and 12^∘,78^∘ are complementary angles.

Q4. Find the angle which is equal to its complement.
Ans: Let the angle equal to its complement be x.
Since the complement of this angle is also x.
Therefore,
The sum of the measures of a complementary angle pair is 90∘.
x + x = 90^∘(complementary angles)
2x = 90^∘
x = 45^∘

Q5. Find the angle which is equal to its supplement.
Ans: Let the angle equal to its supplement be x.
Since the supplement of this angle is also x.
Therefore,
The sum of the measures of a supplementary angle pair is 180^∘ .
x + x = 180^∘
2x = 180^∘
x = 90^∘

Q6. Find the value of x in the following figure.
Ans: From the figure, line l  is parallel to m  and a transversal passes through them. Hence,∠y = 105^∘ (corresponding angles)
∠x + ∠y = 180^∘ (Linear Pair)
∠x = 180^∘ − 105^∘
∠x = 75^∘