Two adjacent angles of a parallelogram are as 2 : 3 find the measures of all angles

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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The measure of two adjacent angles of a parallelogram is in the ratio 2 : 3. Find the measure of each of the angle of the parallelogram.

Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM

Let the adjacent angles of the parallelogram be 2x and 3x.

We know that sum of adjacent angles of a parallelogram is 180o.

⇒ 2x + 3x = 180o

⇒ 5x = 180o

⇒ x = 36o

Therefore, adjacent angles are 2 × 36o = 72o and 3 × 36o = 108o

We know that the opposite angles of a parallelogram are equal.

Thus, the angles of the parallelogram are 72o, 108o, 72o, 108o.

Answered by | 04 Jun, 2014, 03:23: PM

Text Solution

Solution : Given:<br>Two adjacent angles of a parallelogram are as `2: 3.`<br>Let the two adjacent angles be `2x` and `3x`.<br>As we know in parallelogram the sum of adjacent angles is equal to `180^@`.<br>`therefore 2x+3x=180^@`<br>`5x=180^@`<br>`x=180^@/5`<br>`x=36^@`<br>The measure of angles are,<br>`2x=2times36^@=72^@`<br>`3x=3times36^@=108^@`<br>Hence, the measure of adjacent angles are `72^@` and `108^@`.

Two adjacent angles of a parallelogram are as 2: 3. Find the measures of all the angles of a parallelogram.

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