Question

The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. find the measure of each of the angtes of the parallelogram.

Answer 1

in a parallelogram opposite angles are equal
let the two adjacent angles of the parallelogram be 3 X and 2 X
3 X + 2 X + 3 X + 2 X = 360°
( angle sum property of parallelograms)
10 X= 360°
X=36°
angles of parallelogram are 3 ×36=108°
and 2×36=72°
and angles are 108 degree, 72 degree, 108 degree and 72 degree

Answer 2

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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.

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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