In parallelogram WXYZ, the interior angle of X measures 35 degrees and the interior angle of Z also measures 35 degrees. What are the interior angle measures of W and Y?

Question

The interior angle of W measures ____ degrees and the interior angle of Y measures ____ degrees,

Answer 1

In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Since angles X and Z both measure 35 degrees, angles W and Y will be equal to each other and supplementary to angles X and Z.

1. Knowing the angle at X: $$\text{Angle W}+\text{Angle X}={180}^{\circ }$$ $$\text{Angle W}+{35}^{\circ }={180}^{\circ }$$ $$\text{Angle W}={180}^{\circ }-{35}^{\circ }={145}^{\circ }$$

2. Since angle Y is opposite angle W, we have: $$\text{Angle Y}=\text{Angle W}={145}^{\circ }$$

Therefore, the interior angle of W measures 145 degrees and the interior angle of Y measures 145 degrees.