What is the measure of each interior angle of a parallelogram if its adjacent angles are in the ratio 2 3?

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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If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measures of the angles are a 72∘, 108∘ b 36∘, 54∘ c 80∘, 120∘ d 96∘, 144∘

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Solution:

Given that the adjacent angles of a parallelogram are in the ratio 3:2.

Thus, the angles are 3x and 2x respectively.

We know that the sum of the measures of adjacent angles is 180° for a parallelogram.

∠A + ∠B = 180°

3x + 2x = 180°

5x = 180°

x = 180°/5

x = 36°

Thus, one of the angles = 3x

3(36°) = 108°

The other angle is 2x

2(36°) = 72°

The other two angles are 72° and 108° since opposite angles of a parallelogram are equal.

Thus, the measures of the angles of the parallelogram are 108°, 72°, 108°, and 72°

☛ Check: NCERT Solutions for Class 8 Maths Chapter 3

Video Solution:

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 Question 5

Summary:

The measures of two adjacent angles of a parallelogram are in the ratio 3:2. The measures of each of the angles of the parallelogram are 108°, 72°, 108°, and 72°

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