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 adjacent angles are supplementary (they add up to 180 degrees).

Given:

• Angle X = 35 degrees
• Angle Z = 35 degrees

Since angle X and angle Z are opposite angles, the measures of angles W and Y will also equal the measures of angles X and Z, respectively, due to the property of opposite angles in a parallelogram. Therefore:

• Angle W = Angle Y = 180 degrees - Angle X
• Angle Y = Angle W = 180 degrees - Angle Z

Calculating the measures of angles W and Y:

\[ \text{Angle W} = 180^\circ - 35^\circ = 145^\circ \] \[ \text{Angle Y} = 180^\circ - 35^\circ = 145^\circ \]

So, the measures are:

• The interior angle of W measures 145 degrees.
• The interior angle of Y measures 145 degrees.