Question

The bisectors of any two adjacent angles of a parallelogram intersect at an angle of ___.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let ABCD be parallelogram

$\angle A+\angle B={180}^{\circ }$ [Adjacent angles of parallelogram are supplementary]
$\frac{\angle A}{2}+\frac{\angle B}{2}=\frac{{180}^{\circ }}{2}={90}^{\circ }$ [Bisectors divide the angles into half]
$\angle AOB=180-\frac{\angle A}{2}+\frac{\angle B}{2}={90}^{\circ }$