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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