Two adjacent angles on a line are in the ratio 2 3 then the smaller angle is

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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°

☛ Related Questions:

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If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are ______.

• 72°, 108°

• 36°, 54°

• 80°, 120° 

• 96°, 144°

If two adjacent angles of a parallelogram are in the ratio 2 : 3, then the measure of angles are 72°, 108°.

Explanation:

Let the angles be 2x, 3x

The adjacent angles of a parallelogram are always supplementary and the opposite angles are always equal

2x + 3x = 180°

⇒ 5x = 180°

⇒ x = 36°

So, the angles are

2 × 36 = 72°

3 × 36 = 108°

Concept: Properties of a Parallelogram - Property: The adjacent angles in a parallelogram are supplementary.

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