find the value of x in the adjacent figure, if AO and BO are bisector of angle "a" and angle "b"

solution
$\angle D={120}^{\circ },\angle C={130}^{\circ }$
OA and OB are the bisectors of $\angle A$ and $\angle B$.
In quadrilateral ABCD,
$\angle A+\angle B+\angle C+\angle D={360}^{\circ }$
(Sum of angles of a quadrilateral)
$\Rightarrow \angle A+\angle B+{130}^{\circ }+{120}^{\circ }={360}^{\circ }\angle A+\angle B+{250}^{\circ }={360}^{\circ }\angle A+\angle B={360}^{\circ }-{250}^{\circ }={110}^{\circ }$
and $\frac{1}{2}\angle A+\frac{1}{2}\angle B=\frac{{210}^{\circ }}{2}={55}^{\circ }$
$(\because$ OA and OB are bisector of $\angle A$ and $\angle B$ respectively )
$\angle \mathrm{OA}B+\angle OBA={55}^{\circ }\Rightarrow \angle \mathrm{OA}B+\angle OBA+\angle \mathrm{AO}B={180}^{\circ }$
(Sum of angles of a triangle)
$\Rightarrow {55}^{\circ }+\angle A\mathrm{OB}={180}^{\circ }\Rightarrow \angle A\mathrm{OB}={180}^{\circ }-{55}^{\circ }={125}^{\circ }\therefore \angle A\mathrm{OB}={125}^{\circ }$