Question

9. 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.​

Answer 1

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

∠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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