Question

in the figure below, $\triangle efg$ is drawn. the line $\overleftrightarrow{hei}$ is drawn such that $\overleftrightarrow{hei} \parallel \overline{fg}$.
m$\angle efg = $ m$\angle feh$ because they are alternate interior angles.
m$\angle fge = \quad$ because they are\quad

Explanation:

Since $\overleftrightarrow{HEI} \parallel \overleftrightarrow{FG}$, the angle corresponding to $\angle FGE$ is $\angle G EI$ (or $\angle EIG$ is incorrect; the correct alternate interior angle with $\angle FGE$ is $\angle GEI$). Alternate interior angles are congruent when two parallel lines are cut by a transversal, here the transversal is $EG$.

Answer:

$\boldsymbol{m\angle FGE = m\angle GEI}$ because they are alternate interior angles