Question

transversal $overleftrightarrow{cd}$ cuts parallel lines $overleftrightarrow{pq}$ and $overleftrightarrow{rs}$ at points $x$ and $y$, respectively. points $p$ and $r$ lie on one side of $overleftrightarrow{cd}$, while $q$ and $s$ lie on the other side. if $mangle pxy = 64.36^{circ}$, what is $mangle xys$?

a. $180^{circ}$
b. $115.64^{circ}$
c. $64.36^{circ}$
d. $25.64^{circ}$

Explanation:

Step1: Recall angle - relationship

When a transversal cuts two parallel lines, consecutive interior angles are supplementary. $\angle PXY$ and $\angle XYS$ are consecutive interior angles.

Step2: Use the supplementary - angle formula

The sum of two supplementary angles is $180^{\circ}$. Let $m\angle PXY = 64.36^{\circ}$ and $m\angle XYS=x$. Then $m\angle PXY + m\angle XYS=180^{\circ}$, so $x = 180^{\circ}-m\angle PXY$.

Step3: Calculate the value of $m\angle XYS$

Substitute $m\angle PXY = 64.36^{\circ}$ into the formula: $x=180 - 64.36=115.64^{\circ}$.

Answer:

B. $115.64^{\circ}$