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

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

Step-by-step 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

solve for x

Find the measure of the other interior angle of parallelogram

Remember that consecutive interior angles are supplementary

substitute the value of x

solve for y

therefore

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

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