Ex 3.3, 5 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.Let the parallelogram be ABCD
Given, adjacent angles are in the ratio 3 : 2
Let these two angles be ∠A and ∠B
(∠ 𝐴)/(∠ 𝐵) = 3/2
Let ∠A = 3x and ∠B = 2x
We know that
Adjacent angles of a Parallelogram are Supplementary.
∠A + ∠B = 180°
3x + 2x = 180°
5x = 180°
x = (180°)/5
x = 36°
Therefore,
∠A = 3x = 3 × 36° = 108°
∠B = 2x = 2 × 36° = 72°
Now,
Opposite angles of a Parallelogram are equal .
∠C = ∠ A = 108°
∠ B = ∠ D = 72°
∴ Therefore,
∠ A = 108° , ∠B = 72°, ∠C = 108° and ∠D = 72°

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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