Question

In a quadrilateral $ABCD,\angle A$ and $\angle C$ are of of equal measure; $\angle B$ is supplementary to $\angle D$. Find the measure of $\angle A$ and $\angle C$

Answer 1

We are given $\angle B+\angle D={180}^{\circ }$. Using angle-sum property of a quadrilateral, we get
$\angle A+\angle C={360}^{\circ }-{180}^{\circ }={180}^{\circ }$.
Since $\angle A$ and $\angle C$ are of equal measure, we obtain $\angle A=\angle C=\frac{{180}^{\circ }}{2}={90}^{\circ }$