Question

transversal $overleftrightarrow{ef}$ cuts parallel lines $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$ as shown in the diagram, and $mangle 4 = 55.1^circ$. what are $mangle 5$ and $mangle 7$?
a. $mangle 5 = 34.9^circ$, and $mangle 7 = 145.1^circ$.
b. $mangle 5 = 55.1^circ$, and $mangle 7 = 34.9^circ$,
c. $mangle 5 = 124.9^circ$, and $mangle 7 = 55.1^circ$.
d. $mangle 5 = 55.1^circ$, and $mangle 7 = 124.9^circ$.
e. $mangle 5 = 34.9^circ$, and $mangle 7 = 55.1^circ$.

Explanation:

Step1: Find $m\angle5$ (alternate interior)

$\angle4$ and $\angle5$ are alternate interior angles, so $m\angle5 = m\angle4 = 55.1^\circ$

Step2: Find $m\angle7$ (supplementary to $\angle5$)

$\angle5$ and $\angle7$ are supplementary, so $m\angle7 = 180^\circ - m\angle5 = 180^\circ - 55.1^\circ = 124.9^\circ$

Answer:

D. $m\angle5 = 55.1^\circ$, and $m\angle7 = 124.9^\circ$.