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.$mangle ihk + x^circ + mangle jhl = 180^circ$ because the three angles form a straight line.so the value of $x$ must be

Explanation:

Step1: Identify alternate interior angles

From the given parallel lines, $m\angle HIJ = m\angle IHK = 58^\circ$, and $m\angle IJH = m\angle JHL = 39^\circ$.

Step2: Use straight line angle sum

The three angles at $H$ form a straight line, so their sum is $180^\circ$.
$58^\circ + x^\circ + 39^\circ = 180^\circ$

Step3: Calculate $x$

First sum the known angles: $58 + 39 = 97$. Then solve for $x$:
$x = 180 - 97$

Answer:

$83^\circ$