Question

the shape w x y z below is a parallelogram. what is the measure of ∠w? (note that the figure is not drawn to scale.)

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - angles are equal.

Step2: Identify opposite angles

In parallelogram \(WXYZ\), \(\angle W\) and \(\angle Y\) are opposite angles, and \(\angle X\) and \(\angle Z\) are opposite angles.

Step3: Use the angle - sum property

The sum of adjacent angles in a parallelogram is \(180^{\circ}\). \(\angle Z\) and \(\angle W\) are adjacent angles. Given \(\angle Z = 43^{\circ}\), then \(\angle W=180^{\circ}-\angle Z\).
\[

$$\begin{align*} \angle W&=180 - 43\\ &=137^{\circ} \end{align*}$$

\]

Answer:

\(137^{\circ}\)