Question

In given figure,OP and OQ bisects $\angle BOC$ and $\angle AOC$ respectively, then $\angle POQ$ is

• A. ${90}^o$
• B. ${45}^o$
• C. ${135}^o$
• D. ${180}^o$

Answer 1

The correct option is A ${90}^o$

Here OP bisect $\angle BOC$

$\therefore \angle POC=\angle BOP$ …………(i)

and OQ bisect $\angle AOC$

$\therefore \angle AOQ=\angle COQ$ …………….(ii)

and $\angle AOB={180}^o$ [$\because AOB$ is a straight line]

$\Rightarrow \angle BOP+\angle DOC+\angle COQ+\angle AOQ={180}^o$

$\Rightarrow \angle POC+\angle POC+\angle COQ+\angle COQ={180}^o$ [using (i) & (ii)]

$\Rightarrow 2\angle POC+2\angle COQ={480}^o$

$\Rightarrow 2(\angle POC+\angle COQ)={180}^o$

$\Rightarrow 2\angle POQ={180}^o$

$\Rightarrow \angle POQ={90}^o$.