Question

transversal $overleftrightarrow{ef}$ cuts parallel lines $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$ as shown in the diagram, and $mangle4 = 55.1^{circ}$. what are $mangle5$ and $mangle7$?
a. $mangle5 = 34.9^{circ}$, and $mangle7 = 145.1^{circ}$.
b. $mangle5 = 55.1^{circ}$, and $mangle7 = 34.9^{circ}$.
c. $mangle5 = 124.9^{circ}$, and $mangle7 = 55.1^{circ}$.
d. $mangle5 = 55.1^{circ}$, and $mangle7 = 55.1^{circ}$.
e. $mangle5 = 55.1^{circ}$, and $mangle7 = 124.9^{circ}$.

Explanation:

Step1: Identify angle - relationship for ∠5

∠4 and ∠5 are alternate - interior angles. When a transversal cuts two parallel lines, alternate - interior angles are congruent. So, m∠5=m∠4.
m∠5 = 55.1°

Step2: Identify angle - relationship for ∠7

∠4 and ∠7 are corresponding angles. When a transversal cuts two parallel lines, corresponding angles are congruent. So, m∠7=m∠4.
m∠7 = 55.1°

Answer:

D. m∠5 = 55.1°, and m∠7 = 55.1°