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.​

Answer 1

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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

Answer 2

Answer:-

☞Let two adjacent angles A and B of ∥gm

☞ ABCD be 3x and 2x respectively.

☞Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180

⇒3x+2x=180

⇒5x=180

⇒x= 5180 =36

∴∠3×36 =108

and, ∠B=2×36

=72

☞Since the opposite angles are equal in a parallelogram, therefore, ∠C=∠A=108 and ∠D=∠B=72

☞Hence, ∠A=108 ,∠B=72,∠C=108 and ∠D=72

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hope it helps you

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