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

Answer 1

In a parallelogram, opposite angles are equal, and the sum of the interior angles is 360 degrees.

Given that:
- Angle X = 35 degrees
- Angle Z = 35 degrees

We know that angle W and angle Y are opposite angles to angles X and Z, respectively. Therefore:

- Angle W = Angle Y (opposite angles are equal)

Additionally, since the angles in a parallelogram sum up to 360 degrees:

\[
\text{Angle W} + \text{Angle X} + \text{Angle Y} + \text{Angle Z} = 360 \text{ degrees}
\]

Substituting the known angles:

\[
\text{Angle W} + 35 + \text{Angle W} + 35 = 360
\]

This simplifies to:

\[
2 \cdot \text{Angle W} + 70 = 360
\]

Subtracting 70 from both sides:

\[
2 \cdot \text{Angle W} = 290
\]

Now, dividing by 2:

\[
\text{Angle W} = 145 \text{ degrees}
\]

Since angle W = angle Y, we have:

\[
\text{Angle Y} = 145 \text{ degrees}
\]

In conclusion:
- The interior angle of W measures 145 degrees.
- The interior angle of Y measures 145 degrees.