Question

Ray PQ and ray PR are perpendicular to each other. Points B and A are in the interior and exterior of ∠QPR respectively. Ray PB and ray PA are perpendicular to each other. Draw a figure showing all these rays and write -

1. A pair of complementary angles  
2. A pair of supplementary angles. 
3. A pair of congruent angles.

Answer 1

Since ray PQ ⊥ ray PR, then m∠QPR = 90^∘ and ray PA ⊥ ray PB, then m∠APB = 90^∘.

(i) Two angles, sum of whose measures is 90^∘, are called complementary angles.

Here, m∠QPR = 90^∘

⇒ m∠BPQ + m∠BPR = 90^∘

∴ ∠BPQ and ∠BPR are complementary angles.

(ii) Two angles, sum of whose measures is 180^∘, are called supplementary angles.

⇒ m∠APB + m∠QPR 

= 90^∘ + 90^∘ 

= 180^∘

∴ ∠APB and ∠QPR are supplementary angles.

(iii) Angles with the same measures are called congruent angles.

Here, m∠QPR = m∠APB = 90^∘

∴ ∠APB and ∠QPR are congruent angles.