Question

If ABCD is a parallelogram, then the angle bisectors of $\angle A$ and $\angle D$ meet at ‘O’. The measure of $\angle AOD$ is ${45}^{\circ }$​.

• A.
• B.

Answer 1

The correct option is B


$Let\angle A=x^{\circ }then\angle D=(180-x{)}^{\circ }$
(Since the adjacent angles of a parallelogram sum up to ${180}^{\circ })$
$\therefore \frac{\angle A}{2}=\frac{x}{2}$
$and\frac{\angle D}{2}=\frac{(180-x)}{2}=90-\frac{x}{2}$
$\angle AOD=180-[\frac{x}{2}+90-\frac{x}{2}]$
$or\angle AOD=180-90={90}^{\circ }$
$\therefore$ The measure of $\angle AOD$ is ${90}^{\circ }$.