#### 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.

#### Solution

Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3:2. Let ∠A = 3*x* and ∠B = 2*x*

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

∠A + ∠B = 180º

3*x* + 2*x* = 180º

5*x* = 180º

`x = 180^@/5 = 36`

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

∠B = ∠D = 2*x* = 72º (Opposite angles)

Thus, the measures of the angles of the parallelogram are 108º, 72º, 108º, and 72º

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Solution 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 Concept: Kinds of Quadrilaterals - Elements of a Parallelogram.