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

∠W and ∠Y are opposite angles in parallelogram WXYZ. Since opposite angles of a parallelogram are equal, if m∠W = 56°, then m∠Y=56°.

Step3: Find the measure of ∠Z

∠W and ∠Z are adjacent angles in parallelogram WXYZ. Since adjacent angles of a parallelogram are supplementary (the sum of adjacent angles is 180°), and m∠W = 56°, then m∠Z=180° - 56°=124°.

Answer:

1. (Drawing not provided in text - based response, but for drawing: Draw a parallelogram with vertices W, X, Y, Z in order. Mark ∠W at one of the vertices.)
2. m∠Y = 56° because opposite angles of a parallelogram are equal.
3. m∠Z = 124° because adjacent angles of a parallelogram are supplementary (180° - 56° = 124°).