Question

look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarrow{hj}$ are parallel lines and $mangle gfi = 110^{circ}$, what is $mangle hif$?

Explanation:

Step1: Identify angle - type relationship

$\angle GFI$ and $\angle HIF$ are alternate - interior angles.

Step2: Apply the property of alternate - interior angles

For parallel lines $EG$ and $HJ$ cut by a transversal $DK$, alternate - interior angles are congruent. So $m\angle HIF=m\angle GFI$.

Answer:

$110$