1 In parallelogram \( W X Y Z \), with diagonal \( X Z, m \angle W X Z=81^{\circ} \) and \( m \angle W Z X=28^{\circ} \). What is the measure of \( \angle X Y Z \) ? A. \( 109^{\circ} \) B. \( 62^{\circ} \) C. \( 71^{\circ} \) D. \( 90^{\circ} \)

To find the measure of \( \angle X Y Z \) in parallelogram \( W X Y Z \), we can follow these steps: 1. **Identify the known angles**: We have \( m \angle W X Z = 81^{\circ} \) and \( m \angle W Z X = 28^{\circ} \). 2. **Use the properties of triangles**: In triangle \( W X Z \), the sum of the angles is \( 180^{\circ} \). Therefore, we can find \( m \angle W Z Y \) (which is the same as \( m \angle X Y Z \)) using the following equation: \[ m \angle W X Z + m \angle W Z X + m \angle W Z Y = 180^{\circ} \] 3. **Substituting the known values**: \[ 81^{\circ} + 28^{\circ} + m \angle W Z Y = 180^{\circ} \] 4. **Calculate \( m \angle W Z Y \)**: \[ m \angle W Z Y = 180^{\circ} - (81^{\circ} + 28^{\circ}) \] \[ m \angle W Z Y = 180^{\circ} - 109^{\circ} \] \[ m \angle W Z Y = 71^{\circ} \] 5. **Conclusion**: Since \( m \angle W Z Y \) is the same as \( m \angle X Y Z \), we find that: \[ m \angle X Y Z = 71^{\circ} \] Thus, the measure of \( \angle X Y Z \) is \( \boxed{71^{\circ}} \).