Question

a parallelogram wxyz is given. the angle measure of ∠w is 56°. 1. draw and label wxyz and ∠w. 2. what is the angle measure of ∠y? explain how you know. 3. what is the angle measure of ∠z? explain how you know.

Explanation:

Step1: Recall parallelogram properties

In a parallelogram, opposite - angles are equal and adjacent - angles are supplementary.

Step2: Find the measure of ∠Y

Since ∠W and ∠Y are opposite angles in parallelogram WXYZ, by the property of opposite - angles being equal in a parallelogram, \(m\angle Y=m\angle W\). Given \(m\angle W = 56^{\circ}\), so \(m\angle Y=56^{\circ}\).

Step3: Find the measure of ∠Z

Since ∠W and ∠Z are adjacent angles in parallelogram WXYZ, and adjacent angles in a parallelogram are supplementary (i.e., their sum is \(180^{\circ}\)). Let \(m\angle Z=x\). Then \(m\angle W + x=180^{\circ}\). Substituting \(m\angle W = 56^{\circ}\), we get \(x = 180^{\circ}-56^{\circ}=124^{\circ}\), so \(m\angle Z = 124^{\circ}\).

Answer:

1. \(m\angle Y = 56^{\circ}\) because opposite angles in a parallelogram are equal.
2. \(m\angle Z = 124^{\circ}\) because adjacent angles in a parallelogram are supplementary (\(180 - 56=124\)).