Question

In the given figure :
$\angle \text{BOC}=\angle \text{DOC}={34}^{\circ }\text{and}\angle \text{AOD}={120}^{\circ }$
Find $\text{angle AOB and angle AOC}$

Answer 1

Given $\angle \text{BOC}=\angle \text{DOC}={34}^{\circ },\angle \text{AOD}={120}^{\circ }$
To find :$\angle \text{AOB and}\angle \text{AOC}$

$\text{Given}\angle \text{AOD}={120}^{\circ }$
$=\angle \text{(AOB+BOC+DOC)}={120}^{\circ }$[from figure]
$=\angle \text{AOB}+{34}^{\circ }+{34}^{\circ }={120}^{\circ }$
$=\angle \text{AOB}={120}^{\circ }-{68}^{\circ }$
$\therefore \angle \text{AOB}={52}^{\circ }$

Also ,$\angle \text{AOC =AOB+BOC}$ [from figure]
$=\angle \text{AOC}={52}^{\circ }+{34}^{\circ }$
$\therefore \angle \text{AOC}={86}^{\circ }$
hence $\angle \text{AOB}={52}^{\circ }\text{and}\angle \text{AOC}={86}^{\circ }$