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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 - Mathematics

Question

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.

Solution

Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3:2. Let ∠A = 3x and ∠B = 2x

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

∠A + ∠B = 180º

3x + 2x = 180º

5x = 180º

`x = 180^@/5 = 36`

∠A = ∠C = 3x = 108º (Opposite angles)

∠B = ∠D = 2x = 72º (Opposite angles)

Thus, the measures of the angles of the parallelogram are 108º, 72º, 108º, and 72º

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 8 (2018 (Latest))
Chapter 3: Understanding Quadrilaterals
Exercise 3.3 | 5 | Page no. 51
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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 Concept: Types of Quadrilaterals - Properties of a Parallelogram.
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