Question

In the parallelogram, $ABCD$ the bisectors of $\angle A$ and $\angle B$ meet at $O.$ Find $\angle AOB.$

Answer 1

In parallelogram $ABCD,$ $AO$ and $BO$ are angles bisector of $A$ and $B$.

As we know that, the sum of the adjacent angles of a parallelogram is equal to ${180}^{\circ }.$ So,

$2x+2y={180}^{\circ }$

$\Rightarrow x+y={90}^{\circ }$

Now, by using angle sum property in $△AOB,$

${90}^{\circ }+\angle AOB={180}^{\circ }$

$\Rightarrow \angle AOB={90}^{\circ }$