Question

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

(i) A pair of complementary angles (ii) A pair of supplementary angles. (iii) 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 complemenatry angles.

(ii) Two angles, sum of whose measures is 180^∘, are called supplementary angles.
Here, m∠APB + m∠QPR = 90^∘ + 90^∘ = 180^∘
∴ ∠APB and ∠QPR are supplemenatry angles.

(iii) Angles with exactly the same measures are called congruent angles.
Here, m∠QPR = m∠APB = 90^∘
∴ ∠APB and ∠QPR are congruent angles.