Question

look at this diagram: if (overleftrightarrow{eg}) and (overleftrightarrow{hj}) are parallel lines and (mangle hik = 111^{circ}), what is (mangle jif)?

Explanation:

Step1: Identify vertical - angle relationship

$\angle HIK$ and $\angle JIF$ are vertical angles.

Step2: Apply vertical - angle property

Vertical angles are congruent, so $m\angle JIF=m\angle HIK$.

Answer:

$111$