Question

in parallelogram wxyz, with diagonal xz, ( mangle wxz = 81^{circ} ) and ( mangle wzx = 28^{circ} ). what is the measure of ( angle xyz )?
a. ( 71^{circ} )
b. ( 62^{circ} )
c. ( 90^{circ} )
d. ( 109^{circ} )

Explanation:

Step1: Find \(m\angle W\) in \(\triangle WXZ\)

In \(\triangle WXZ\), use the angle - sum property of a triangle (\(m\angle A + m\angle B+m\angle C = 180^{\circ}\)). Let \(m\angle WXZ=\alpha = 81^{\circ}\), \(m\angle WZX=\beta=28^{\circ}\), and \(m\angle W = \gamma\). Then \(\gamma=180^{\circ}-(\alpha+\beta)\).
Substitute \(\alpha = 81^{\circ}\) and \(\beta = 28^{\circ}\): \(\gamma=180-(81 + 28)=180 - 109=71^{\circ}\).

Step2: Use the property of a parallelogram

In a parallelogram \(WXYZ\), \(\angle W\) and \(\angle XYZ\) are opposite angles.
By the property of a parallelogram (opposite angles of a parallelogram are equal), \(m\angle XYZ=m\angle W\).

Answer:

A. \(71^{\circ}\)