Question

In the given figure, ABCD is a quadrilateral and AO and DO are bisectors of $\angle Aand\angle D$. The value of 'x ' is

• A. ${70}^{\circ }$
• B. ${85}^{\circ }$
• C. ${95}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is C ${95}^{\circ }$

In a quadrilateral ABCD, AO and DO are bisectors of $\angle Aand\angle D$
$\angle A+\angle B+\angle C+\angle D={360}^{\circ }$ ($\because$ Sum of angles in quadrilateral = 360${}^{\circ }$)
$\Rightarrow \angle A+{70}^{\circ }+{120}^{\circ }+\angle D={360}^{\circ }$
$\Rightarrow \angle A+\angle D={170}^{\circ }$
$\Rightarrow \frac{\angle A}{2}+\frac{\angle D}{2}=\frac{{170}^{\circ }}{2}$
$\Rightarrow \frac{\angle A}{2}+\frac{\angle D}{2}={85}^{\circ }$
In $\Delta AOD,$
$\angle AOD={180}^{\circ }-(\frac{\angle A}{\angle 2}+\frac{\angle D}{\angle 2})$ ($\because$ Sum of angles in triangle = 180${}^{\circ }$)
$\angle AOD={180}^{\circ }-{85}^{\circ }$
$\angle AOD={95}^{\circ }$
Hence, the value of '$x$ 'is ${95}^{\circ }$.