Question

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.

So, ∠A = ∠C

∠B = ∠D

And ∠A + ∠C = 180°, ∠B + ∠D = 180°

Now, ∠A + ∠A = 180°  ...[∠C = ∠A]

⇒ 2∠A = 180°

⇒ ∠A = 90°

Similarly, ∠B = 90°

Hence, each angle is a right angle.