Question

look at this diagram: if $overleftrightarrow{df}$ and $overleftrightarrow{gi}$ are parallel lines and $mangle ihj = 120^{circ}$, what is $mangle feh$?

Explanation:

Step1: Identify vertical - angle relationship

$\angle IHJ$ and $\angle EHG$ are vertical angles, so $m\angle EHG=m\angle IHJ = 120^{\circ}$.

Step2: Use corresponding - angle property

Since $\overleftrightarrow{DF}$ and $\overleftrightarrow{GI}$ are parallel lines, $\angle FEH$ and $\angle EHG$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are congruent. So $m\angle FEH=m\angle EHG$.

Answer:

$120$