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)

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 that the angle at \( X \) measures \( 35^\circ \), the opposite angle at \( Z \) also measures \( 35^\circ \).

To find the measures of angles \( W \) and \( Y \):

1. Since angles \( X \) and \( W \) are adjacent, they must sum to \( 180^\circ \): \[ W + X = 180^\circ \] Therefore: \[ W + 35^\circ = 180^\circ \] Solving for \( W \): \[ W = 180^\circ - 35^\circ = 145^\circ \]

2. Since angles \( Y \) and \( Z \) are opposite, they are equal. Thus: \[ Y = Z = 35^\circ \]

So the measures are:

• The interior angle of \( W \) measures \( 145^\circ \).
• The interior angle of \( Y \) measures \( 145^\circ \).

In summary:

• The interior angle of \( W \) measures 145 degrees.
• The interior angle of \( Y \) measures 145 degrees.