Question

the shape wxyz below is a parallelogram. what is the measure of ∠x? (the figure is not drawn to scale.)

Explanation:

Step1: Recall parallelogram property

In a parallelogram, adjacent - angles are supplementary, i.e., the sum of adjacent angles is 180°. $\angle Z$ and $\angle X$ are adjacent angles in parallelogram $WXYZ$.

Step2: Set up the equation

Let $\angle Z = 40^{\circ}$. We know that $\angle Z+\angle X=180^{\circ}$.

Step3: Solve for $\angle X$

$\angle X = 180^{\circ}-\angle Z$. Substitute $\angle Z = 40^{\circ}$ into the equation: $\angle X=180 - 40=140^{\circ}$.

Answer:

$140^{\circ}$