Question

select the correct answer.
transversal cd cuts parallel lines pq and rs at points x and y, respectively. points p and r lie on one side of cd, while q and s lie on the
other side. if m∠pxy = 64.36°, what is m∠xys?
a. 180°
b. 115.64°
c. 64.36°
d. 25.64°

Explanation:

Step1: Use the property of consecutive interior angles

When a transversal cuts parallel lines, consecutive interior angles are supplementary. That is, \(\angle PXY+\angle XYS = 180^{\circ}\)

Step2: Solve for \(\angle XYS\)

Given \(\angle PXY=64.36^{\circ}\), then \(\angle XYS=180^{\circ}-\angle PXY\)
Substitute the value of \(\angle PXY\): \(\angle XYS = 180 - 64.36\)
\(\angle XYS=115.64^{\circ}\)

Answer:

B. \(115.64^{\circ}\)