Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle deh = 50^{circ}$, what is $mangle fec$?

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle DEH$ and $\angle FEC$ are vertical angles.

Step2: Apply vertical - angle property

Since vertical angles are congruent, if $m\angle DEH = 50^{\circ}$, then $m\angle FEC=m\angle DEH$.

Answer:

$50^{\circ}$