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

Answer:

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180

⇒3x+2x=180

⇒5x=180

⇒x=5/180=36

∴∠3×36=108

and, ∠B=2×36=72

Since the opposite angles are equal in a parallelgram, therefore, 

∠C=∠A=108 and ∠D=∠B=72

Hence, ∠A=108,∠B=72,∠C=108

 and ∠D=72

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