Question

in the figure below, $\triangle efg$ is drawn. the line $\overleftrightarrow{hei}$ is drawn such that $\overleftrightarrow{hei} \parallel \overline{fg}$.

$\text{m}\angle efg = \text{m}\angle feh$ because they are alternate interior angles.

$\text{m}\angle fge = \text{m}\angle gei$ because they are alternate interior angles.

$\text{m}\angle feh + x^\circ + \text{m}\angle gei = \quad$ because the
three angles $\quad$

Explanation:

Step1: Identify straight angle sum

A straight angle measures $180^\circ$. The angles $\angle FEH$, $x^\circ$, and $\angle GEI$ form a straight line at point $E$, so their sum equals $180^\circ$.

Step2: Match angle relationships

From the given alternate interior angle pairs: $\angle FEH = 56^\circ$ and $\angle GEI = 71^\circ$. The three angles lie on a straight line, meaning they are supplementary (sum to a straight angle).

Answer:

First blank: $\boldsymbol{180^\circ}$
Second blank: $\boldsymbol{form a straight angle}$