The measures of two adjacent angles of a parallelogram are in the ratio 3:2 Find the measure of each - Maths - Understanding Quadrilaterals

Question

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

Gopal Mohanty · Accepted Answer

Let the measures of two adjacent angles, ∠A and ∠B,
of parallelogram ABCD are in the ratio of 3:2 Let ∠A =
3x and ∠B = 2x
We know that the sum of the measures of adjacent angles is
180º for a parallelogram
∠A + ∠B = 180º
3x + 2x = 180º
5x = 180º
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∠A = ∠C = 3x = 108º (Opposite
angles)
∠B = ∠D = 2x = 72º (Opposite angles)
Thus, the measures of the angles of the parallelogram are
108º, 72º, 108º, and 72º

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.