Question

Use the angle shown to determine if the line are parallel

Answer 1

If the lines were parallel then

angle H would be corresponding to angle L and then

$\measuredangle H\cong\measuredangle Z.$

Since angles H and Z are a linear pair then if the lines were parallel angle H, Z and L would have to be right angles. Since the problem never states that those angles are right angles, then the lines are not necessarily parallel.

Answer: No.