Question

n 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
𝑊
measures degrees and the interior angle of Y
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 \( X = 35^\circ \)
- Angle \( Z = 35^\circ \)

Since opposite angles are equal, we have:
- Angle \( Y = W \)

Since adjacent angles are supplementary, we can calculate the measures of angles \( W \) and \( Y \):

\[
\text{Angle } W + \text{Angle } X = 180^\circ
\]
\[
\text{Angle } W + 35^\circ = 180^\circ
\]

Subtracting \( 35^\circ \) from both sides:
\[
\text{Angle } W = 180^\circ - 35^\circ = 145^\circ
\]

Since angle \( Y \) is equal to angle \( W \):
\[
\text{Angle } Y = 145^\circ
\]

Therefore, the interior angles are:
- The interior angle of \( W \) measures \( 145^\circ \)
- The interior angle of \( Y \) measures \( 145^\circ \)

Final answer:
- The interior angle of \( W \) measures \( 145^\circ \) and the interior angle of \( Y \) measures \( 145^\circ \).