Question

5
in parallelogram wxyz, with diagonal xz, m∠wxz = 81° and m∠wzx = 28°. what is the measure of ∠xyz?
a. 90°
b. 62°
c. 71°
d. 109°

Explanation:

Step1: Use property of parallelogram

In parallelogram \(WXYZ\), \(WX\parallel YZ\). So, \(\angle WXZ=\angle YZX\) (alternate - interior angles). Also, we know that \(\angle W = 180^{\circ}-(\angle WXZ+\angle WZX)\) (angle - sum property of a triangle in \(\triangle WXZ\)). But since \(WX\parallel YZ\), \(\angle XYZ=\angle W\) (opposite angles of a parallelogram are equal). First, find \(\angle W\) in \(\triangle WXZ\).

Step2: Calculate \(\angle W\)

Using the angle - sum property of a triangle (\(\angle A+\angle B+\angle C = 180^{\circ}\)) in \(\triangle WXZ\), where \(\angle WXZ = 81^{\circ}\) and \(\angle WZX=28^{\circ}\). Then \(\angle W=180^{\circ}-(81^{\circ}+28^{\circ})\).

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Step3: Use property of parallelogram (opposite angles)

Since in parallelogram \(WXYZ\), \(\angle XYZ=\angle W\) (opposite angles of a parallelogram are equal).

Answer:

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