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 = $ $\boldsymbol{\text{dropdown}}$ because they are $\boldsymbol{\text{dropdown}}$

answer
attempt 1 out of 2
you must answer all questions above in

Explanation:

Step1: Identify alternate interior angles

Since $\overleftrightarrow{HEI} \parallel \overline{FG}$ and $\overline{EF}$ is a transversal, $\angle HEF$ and $\angle EFG$ are alternate interior angles, so $m\angle HEF = m\angle EFG = 56^\circ$.

Step2: Identify another pair of alternate interior angles

Since $\overleftrightarrow{HEI} \parallel \overline{FG}$ and $\overline{EG}$ is a transversal, $\angle IEG$ and $\angle EGF$ are alternate interior angles, so $m\angle IEG = m\angle EGF = 71^\circ$.

Step3: Calculate $x$ using straight angle

The angles $\angle HEF$, $x$, and $\angle IEG$ form a straight angle ($180^\circ$).
$$x = 180^\circ - 56^\circ - 71^\circ$$
$$x = 53^\circ$$

Step4: Address the dropdown question

For $m\angle EFG$, the measure is equal to the alternate interior angle formed by transversal $\overline{EF}$ with the parallel lines.

Answer:

$m\angle EFG = 56^\circ$ because they are alternate interior angles
$x = 53^\circ$