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 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

∠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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