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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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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Question 31 If two adjacent angles of a parallelogram are in the ratio 2: 3, then the measures of the angles area 72∘, 108∘b 36∘, 54∘c 80∘, 120∘d 96∘, 144∘
Solution
Given, two adjacent angles of a parallelogram are in the ratio 2 : 3 Let the angles be 2x and 3x. Then,
2x+3x=180∘ [∵ adjacent angles of a parallelogram are supplementary]
⇒5x=180∘⇒x=36∘
Hence, the measures of the angles are 2x=2×36∘=72∘ and 3x=3×36∘=108∘.
Mathematics
NCERT Exemplar
Standard VIII
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