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. $$ 90^{\circ} $$

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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 $$ \boxed{71^{\circ}} $$.
$$ \angle X Y Z = 71^{\circ} $$, choice C.

1
In parallelogram , with diagonal and . What is the measure of ?
A.
B.
C.
D.

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