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.​

Answer 1

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

Let ∠A = 3x and ∠B = 2x

We know that sum of measure of adjacent angles in parallelogram is 180°.

∠A + ∠B = 180°

3x + 2x = 180°

5x = 180°

x = 180/5 =36°

∠A = ∠C = 3x = 3×36 = 108°..............(opposite angles)

∠B = ∠D = 2x = 2× 36 = 72°..............(opposite angles)

Thus the measures of angles of parallelogram are 108° ,72°, 108°,72°.

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Answer 2

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Let us take the two adjacent angles be 3x & 2x

Note :- Sum of the adjacent angles in a parallelogram is 180°

So, we will simply add up and equal to 180 and will get the value of x

→ 3x + 2x = 180

→ 5x = 180

→ x = 180/5

→ x = 36

Thus, we got the value of x which is 36

Now, we will simply subsitute the values

1st angle :- 3x = 3 × 36 = 108

2nd angle :- 2x = 2 × 36 = 72