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

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}

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