Question

lines ab and cd are parallel. if the measure of ∠y equals 63°, what is the measure of ∠z?
a. 63°
b. 117°
c. 162°
d. 72°

Explanation:

Step1: Identify angle relationship

Since \(AB \parallel CD\) and the transversal creates consecutive interior angles (or supplementary angles on a straight line? Wait, actually, \(\angle y\) and \(\angle z\) are same - side interior angles? Wait, no, looking at the diagram (even though not fully clear, but since \(AB\) and \(CD\) are parallel, and \(\angle y\) and \(\angle z\) should be supplementary. Because consecutive interior angles are supplementary. So if \(\angle y = 63^{\circ}\), then \(\angle z=180^{\circ}-\angle y\).

Step2: Calculate \(\angle z\)

\[

$$\begin{align*} \angle z&=180^{\circ}- 63^{\circ}\\ &=117^{\circ} \end{align*}$$

\]

Answer:

B. \(117^{\circ}\)