In paratlelogram \( W X Y Z \), 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. \( 62^{\circ} \) B. \( 109^{\circ} \) C. \( 90^{\circ} \) D. \( 71^{\circ} \)

To solve for the measure of \( \angle X Y Z \) in the parallelogram \( W X Y Z \), we can use the properties of the angles in a parallelogram and the triangle formed by the diagonal. First, in triangle \( W X Z \): \[ m \angle W X Z + m \angle W Z X + m \angle X W Z = 180^\circ \] Substituting the known angles: \[ 81^\circ + 28^\circ + m \angle X W Z = 180^\circ \] \[ 109^\circ + m \angle X W Z = 180^\circ \] \[ m \angle X W Z = 180^\circ - 109^\circ = 71^\circ \] In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Therefore, \( m \angle X Y Z \) (which is opposite to \( m \angle X W Z \)) is equal to \( m \angle X W Z \). Thus, the measure of \( \angle X Y Z \) is: \[ m \angle X Y Z = 71^\circ \] The correct answer is: D. \( 71^{\circ} \)