Question

the adjacent angle of a parallelogram are in the ratio 3: 2 find the measure of each angle?​

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

o

⇒3x+2x=180

o

⇒5x=180

o

⇒x=

5

180

o

=36

o

∴∠3×36

o

=108

o

and, ∠B=2×36

o

=72

o

Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108

o

and ∠D=∠B=72

o

Hence, ∠A=108

o

,∠B=72

o

,∠C=108

o

and ∠D=72

o

Answer 2

Answer:

let all four angles be A,B,C,D

let the adjacent angles be 3x and 2x, respectively

now , 3x+2x=180. (sum of adjacent angles of parallelogram is supplementary)

=> 5x=180

=> X=180/5

=>X = 36°

so measure of adjacent angles is

3x=3×36=108°

angle A=108°

and second one 2x= 2×36=72°

angle B=72°

now angle A= angle C. ( opposite angles are equal).

so angle C= 108°

and angle B = angle D. ( opposite angles are equal)

so angle D=72°