Question

look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarrow{hj}$ are parallel lines and $mangle efi = 58^{circ}$, what is $mangle jif$?

Explanation:

Step1: Identify angle - type relationship

$\angle EFI$ and $\angle JIF$ are alternate - interior angles.

Step2: Apply property of alternate - interior angles

When two parallel lines are cut by a transversal, alternate - interior angles are congruent. Since $\overleftrightarrow{EG}\parallel\overleftrightarrow{HJ}$ and $\angle EFI$ and $\angle JIF$ are alternate - interior angles, $m\angle JIF=m\angle EFI$.

Answer:

$58$