Mathematics

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


SOLUTION


Ray $$PQ$$ and $$PR $$are perpendicular each other. Point $$B$$ is the interior and Point $$A$$ is the exterior of $$\angle QPR$$. 
Ray $$PB$$ and $$PA$$ are perpendicular to each other. 
$$(i)$$ A pair of Complementary angles:
$$\Rightarrow$$  $$\angle QPB$$ and $$\angle BPR$$ because their sum is $$90^o$$
$$\Rightarrow$$  $$\angle BPR$$ and $$\angle RPA$$ because their sum is $$90^o$$
$$(ii)$$ A pair of Supplementary angles:
$$\Rightarrow$$  $$\angle QPR$$ and $$\angle BPA$$ because their sum is $$180^o$$
$$(iii)$$ A pair of congruent angles:
$$\Rightarrow$$  $$\angle BPA\equiv\angle QPR$$             [ Each angle is $$90^o$$ ]
$$\Rightarrow$$  $$\angle BPA=\angle QPR$$
So, $$\angle RPA+\angle BPR=\angle BPR+\angle QPB$$         [ Using angle addition property ]
So, $$\angle RPA=\angle QPB$$
Hence, $$\angle RPA\equiv \angle QPB$$
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Subjective Medium Published on 09th 09, 2020
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