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.