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:

ok here you go

Step-by-step explanation:

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

.