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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 = 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
`x = 180^circ/5 = 36`
∠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
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