The measures of two adjacent angles of a parallelogram are in the ratio 3: 2. Find the measure of each of the angles of the parallelogram

Question

Philoid · Accepted Answer

Let us consider that the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3: 2

And, ∠A = 3x and ∠B = 2x

We know that the sum of the measures of adjacent angles is 180^o for a parallelogram

∠A + ∠B = 180^o

3x + 2x = 180^o

5x = 180^o

∠A = ∠C = 3x = 108^o (Opposite angles)

∠B = ∠D = 2x = 72^o (Opposite angles)

Hence, the measure of the angles of the parallelogram are 108^o, 72^o, 108^o, and 72^o