Question

Find the angles of a parallelogram in which an exterior angle is one-third that its interior angle.​

Answer 1

The angles of a parallelogram are 135°-45°-135°-45°

Explanation:

we know that

In a parallelogram opposites angles are congruent and consecutive angles are supplementary

Remember that

The sum of a exterior angle and its interior angle is equal to 180 degrees

Let

x ----> the measure of one interior angle of parallelogram

y ----> the measure of the other interior angle of parallelogram

we have that

`x+(x)/(3)=180^o`

solve for x

`(4)/(3)x=180^o\\\\x=(180^o)3/4\\\\x=135^o`

Find the measure of the other interior angle of parallelogram

Remember that consecutive interior angles are supplementary

`x+y=180^o`

substitute the value of x

`135^o+y=180^o`

solve for y

`y=45^o`

therefore

The angles of a parallelogram are 135°-45°-135°-45°