Question

12.
The measures of two adjacent angles of a parallelogram are in the ratio 3:2.
Find the measure of all the angles of the parallelogram?
किसी समान्तर चतुर्भुज के आसन्न कोणों का अनुपात 3:2 है। समान्तर चतुर्भुज के
सभी कोणों का माप ज्ञात कीजिए?​

Answer 1

Answer:

Let the adjacent angles of the parallelogram be 2x and 3x.

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

⇒ 2x + 3x = 180o

⇒ 5x = 180o

⇒ x = 36o

Therefore, adjacent angles are 2 × 36o = 72o and 3 × 36o = 108o

We know that the opposite angles of a parallelogram are equal.

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

Step-by-step explanation:

Answer 2

Let the common ratio be x

3x +2x=180(opposite angles of a parallelogram is parallel and so they are so interior angles)

5x=180

X=180/5

X=36

3x=3×36=108

2x=2×36=72

Opposite angles of a parallelogram are equal