Question

Ray PR and ray PQ are perpendicular to each other. The point B is in the interior of $\angle$QPR and a point A is in the exterior of $\angle$RPQ such that ray PB and ray PA are perpendicular to each other. Draw the figure and write down a pair of (i) Complementary angle (ii) Supplementary angles (iii) Congruent angles.

Answer 1

Given: $\mathrm{RP}\perp \mathrm{PQ}\mathrm{and}\mathrm{PA}\perp \mathrm{PB}$
Then, $\angle \mathrm{RPQ}=90°\mathrm{and}\angle \mathrm{APB}=90°$

Now, we have,
(i) Complementary angles: $\angle \mathrm{APR}\mathrm{and}\angle \mathrm{RPB};\angle \mathrm{RPB}\mathrm{and}\angle \mathrm{BPQ}$
(ii) Supplementary angles: $\angle \mathrm{APB}\mathrm{and}\angle \mathrm{RPQ}$
(iii) Congruent angles: $\angle \mathrm{APR}\mathrm{and}\angle \mathrm{BPQ};\angle \mathrm{APB}\mathrm{and}\angle \mathrm{RPQ}$