Question

two opposite angles of a parallelogram is five seventh of its adjacent angle, find the measure of each interior angle of the parallelogram​

Answer 1

Answer:

Let x and y be two adjacent angles of a parallelogram.

According to the question,

⇒ x=

3

2

y ----- ( 1 )

We know in parallelogram, sum of adjacent angles are supplementary.

∴ x+y=180

o

.

⇒

3

2

y+y=180

o

[ From ( 1 ) ]

⇒ 2y+3y=540

o

⇒ 5y=540

o

⇒ y=108

o

.

Substituting value of y in equation ( 1 ) we get,

⇒ x=

3

2

×108

o

⇒ x=72

o

We know that, in parallelogram opposite angles are equal.

∴ Four angles of parallelogram are 108

o

,72

o

,108

o

and 72

o

.