Question

ABCD is a quadrilateral and AP and DP are bisectors of $\angle Aand\angle D$ . The value of x is :

• A. ${60}^{\circ }$
• B. ${85}^{\circ }$
• C. ${95}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

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

$\angle A+\angle B+\angle C+\angle$ D = 360

$\angle A+\angle D$ = 360 - 130 - 60

$\angle A+\angle D$ = 170

$\frac{\angle A}{2}+\frac{\angle D}{2}$ = 85

Now, $\frac{\angle A}{2}+\frac{\angle D}{2}+\angle x$ = 180

=> $\angle x=95$