Question

in the figure below, $\triangle hij$ is drawn. the line $overleftrightarrow{khl}$ is drawn such that $overleftrightarrow{khl} parallel overline{ij}$.$mangle hij = mangle ihk$ because they are alternate interior angles.$mangle ijh = mangle jhl$ because they are alternate interior angles.$mangle ihk + x^circ + mangle jhl = \boldsymbol{square}$ because the three angles$\boldsymbol{vee}LXB0180^circ$

Explanation:

Step1: Identify angle relationship

$\overleftrightarrow{KHL} \parallel \overline{IJ}$, so $m\angle HJI = m\angle IHK = 39^\circ$, $m\angle JHI = m\angle JHL = 58^\circ$ (alternate interior angles).

Step2: Use straight angle sum rule

The angles $\angle IHK$, $x^\circ$, and $\angle JHL$ form a straight line at point $H$. The sum of angles on a straight line is $180^\circ$.
<Expression>
$m\angle IHK + x^\circ + m\angle JHL = 180^\circ$
</Expression>

Answer:

$180^\circ$