Question

Question 166
Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

Answer 1

Let ABCD be a quadrilateral, such that
$\angle A=\angle C,\angle B=\angle D$ and also $\angle A+\angle C={180}^{\circ },\angle B+\angle D={180}^{\circ }$
Now, $\angle A+\angle A={180}^{\circ }$ [$\because \angle C=\angle A$]
$\Rightarrow 2\angle A={180}^{\circ }\Rightarrow \angle A={90}^{\circ }Similarly,\angle B={90}^{\circ }$
Hence, each angle is a right angle.