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 the sum of the interior angles is 360 degrees.

Given that angle X and angle Z each measure 35 degrees:

1. Since opposite angles are equal, angle Y also measures 35 degrees.
2. To find the measure of angle W, we can use the fact that the sum of the angles in a parallelogram is 360 degrees.

Let the measure of angle W be \( W \). The relationship can be expressed as:

\[
W + X + Y + Z = 360
\]
\[
W + 35 + 35 + 35 = 360
\]
\[
W + 105 = 360
\]
\[
W = 360 - 105
\]
\[
W = 255
\]

Since angles W and Y are opposite angles:

\[
Y = 255 \text{ degrees}
\]

Thus, the interior angle of W measures **255 degrees** and the interior angle of Y measures **35 degrees**.

To summarize:
- The interior angle of W measures **255 degrees**.
- The interior angle of Y measures **35 degrees**.