Question

look at this diagram: if $overleftrightarrow{eg}$ and $overleftrightarrow{hj}$ are parallel lines and $mangle efi = 117^{circ}$, what is $mangle jif$?

Explanation:

Step1: Identify angle - relationship

$\angle EFI$ and $\angle JIF$ are same - side interior angles.

Step2: Recall property of parallel lines

When two parallel lines are cut by a transversal, same - side interior angles are supplementary, i.e., their sum is $180^{\circ}$. So $m\angle EFI + m\angle JIF=180^{\circ}$.

Step3: Solve for $m\angle JIF$

Given $m\angle EFI = 117^{\circ}$, then $m\angle JIF=180^{\circ}-m\angle EFI$. Substitute $m\angle EFI = 117^{\circ}$ into the equation: $m\angle JIF = 180 - 117=63^{\circ}$.

Answer:

$63$