In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (their measures add up to 180 degrees).
Given that:
- Angle X measures 35 degrees.
- Angle Z, being opposite angle X, also measures 35 degrees.
To find the measures of angles W and Y, we can use the property of adjacent angles:
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Angle W is adjacent to angle X: \[ \text{Angle W} + \text{Angle X} = 180 \text{ degrees} \] \[ \text{Angle W} + 35 = 180 \] \[ \text{Angle W} = 180 - 35 = 145 \text{ degrees} \]
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Angle Y is adjacent to angle Z: \[ \text{Angle Y} + \text{Angle Z} = 180 \text{ degrees} \] \[ \text{Angle Y} + 35 = 180 \] \[ \text{Angle Y} = 180 - 35 = 145 \text{ degrees} \]
Thus, the measures are:
- The interior angle of W measures 145 degrees.
- The interior angle of Y measures 145 degrees.
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