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 angles2. A pair of supplementary angles3.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
Questions 120418
Subjects 10
Chapters 88
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