Question

in the figure below, $\triangle hij$ is drawn. the line $overleftrightarrow{khl}$ is drawn such that $overleftrightarrow{khl} parallel overline{ij}$.
$mangle hij = \boxed{}$ because they are

Explanation:

Step1: Identify angle relationship

Since $\overleftrightarrow{KHL} \parallel \overline{IJ}$, $\angle HIJ$ and $\angle KHI$ are consecutive interior angles (same-side interior angles), which are supplementary. First, calculate $\angle HJI$ using triangle angle sum.

Step2: Calculate $\angle HJI$

The sum of angles in a triangle is $180^\circ$. For $\triangle HIJ$:
$$m\angle HJI = 180^\circ - 58^\circ - 39^\circ = 83^\circ$$

Step3: Relate to target angle

$\angle HLJ$ and $\angle HJI$ are alternate exterior angles (since $\overleftrightarrow{KHL} \parallel \overline{IJ}$ and $\overline{HJ}$ is a transversal). Alternate exterior angles are congruent.

Answer:

$m\angle HLJ = 83^\circ$ because they are alternate exterior angles.