Question

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
?(1 point)
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 (their measures add up to 180 degrees).

Given that:
- Angle X measures 35 degrees.
- Angle Z, being opposite angle X, also measures 35 degrees.

To find the measures of angles W and Y, we can use the property of adjacent angles:

1. Angle W is adjacent to angle X:
\[
\text{Angle W} + \text{Angle X} = 180 \text{ degrees}
\]
\[
\text{Angle W} + 35 = 180
\]
\[
\text{Angle W} = 180 - 35 = 145 \text{ degrees}
\]

2. Angle Y is adjacent to angle Z:
\[
\text{Angle Y} + \text{Angle Z} = 180 \text{ degrees}
\]
\[
\text{Angle Y} + 35 = 180
\]
\[
\text{Angle Y} = 180 - 35 = 145 \text{ degrees}
\]

Thus, the measures are:
- The interior angle of W measures **145 degrees**.
- The interior angle of Y measures **145 degrees**.