Question

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

Answer 1

Let x be the measure of two adjacent angles A and B.

We know that the adjacent angles of a parallelogram are supplementary.

∴ ∠P + ∠Q = 180°
or X + x = 180°
or 2x = 180°
or x = 90°
∴ ∠P = 90° and ∠Q = 90°

We know that the opposite angles are equal in a parallelogram

∴ ∠P = ∠Q = ∠R = ∠S = 90°