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 \( 145^\circ \).
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