Question

In a quadrilateral $ABCD,AO$ and $BO$ are the bisectors of $\angle Aand\angle B$ respectively, $\angle C={70}^{\circ }and\angle D={30}^{\circ }$. Then, $\angle AOB=$ ?

(a) ${40}^{\circ }$

(b) ${50}^{\circ }$

(c) ${80}^{\circ }$

(d) ${100}^{\circ }$

Answer 1

Correct option: (b) ${50}^{\circ }$
Explanation:
$\angle C={70}^{\circ }$ and $\angle D={30}^{\circ }$
Then $\angle A+\angle B={360}^{\circ }-(70+30{)}^{\circ }={260}^{\circ }$
$\therefore \frac{1}{2}(\angle A+\angle B)=\frac{1}{2}\left({260}^{\circ }\right)={130}^{\circ }$
In \Delta ​ AOB\), we have:
$\angle AOB={180}^{\circ }-\left[12\right(\angle A+\angle B\left)\right]$
$\Rightarrow \angle AOB=180-130={50}^o$