Question

two opposite angles of a parallelogram are 6x-17° and x+63°. Find the measure of each angle of the parallelogram.​

Answer 1

Step-by-step explanation:

Given :-

Two opposite angles of a parallelogram are 6x-17° and x+63°.

To find:-

Find the measure of each angle of the parallelogram.?

Solution:-

Given that :

Two opposite angles of a parallelogram = (6x-17)° and (x+63)°.

We know that

Opposite angles are equal in a Parallelogram

=> (6x-17)° = (x+63)°

=> 6x° -x° = 63°+17°

=> 5x° = 80°

=>x° = 80°/5

=> x° = 16°

Now ,

6x-17 = 6(16°)-17=96°-17°=79°

x+63°=16°+63°=79°

And

The adjacent angles in a Parallelogram are Supplementary

=> 79° +adjacent angle = 180°

=> adjacent angle of 79° = 180°-79°

Adajacent angle of 79° = 101°

The angles are 79° ,101° ,79° and 101°

Answer:-

The measure of all four angles in the paralellogram are 79° ,101° ,79° and 101°

Used formulae:-

• The adjacent angles in a Parallelogram are Supplementary

• Opposite angles are equal in a Parallelogram.