Question

In figure, ray OC stands on the line AB; ray OL and ray OM are angle bisector of $\angle AOC$ and $\angle BOC$, respectively. Find $\angle LOM$.

• A. ${90}^o$
• B. ${100}^o$
• C. ${80}^o$
• D. ${120}^o$

Answer 1

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

In figure, we have
$\angle AOC+\angle BOC={180}^o$ (Linear pair of angles) ......(1)
Now, ray OL bisects $\angle AOC$, therefore,
$\angle LOC=\frac{1}{2}\angle AOC$ ......(2)
Similarly, $\angle MOC=\frac{1}{2}\angle BOC$ .....(3)
Adding (2) and (3), we have
$\Rightarrow \angle LOC+\angle MOC=\frac{1}{2}\angle AOC+\frac{1}{2}\angle BOC$
$\Rightarrow \angle LOM=\frac{1}{2}\{\angle AOC+\angle BOC\}$
$\Rightarrow \angle LOM=\frac{1}{2}\times {180}^o={90}^o$ [From equation 1]
Therefore, $\angle LOM={90}^o$