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

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=180o

⇒3x+2x=180o

⇒5x=180o

⇒x=5180o=36o

∴∠3×36o=108o

and, ∠B=2×36o=72o

Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108o and ∠D=∠B=72o

Hence, ∠A=108o,∠B=72o,∠C=108o 

and ∠D=72o

Answer 2

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