Question

look at this diagram: if (overleftrightarrow{ln}) and (overleftrightarrow{oq}) are parallel lines and (mangle lmk = 48^{circ}), what is (mangle nmk)?

Explanation:

Step1: Recall angle - relationship for parallel lines

When two parallel lines are cut by a transversal, corresponding angles are equal. $\angle LMK$ and $\angle MPQ$ are corresponding angles.

Step2: Use the given information

We know that $\angle LMK = 48^{\circ}$. Since $\angle LMK$ and $\angle NMP$ are vertical - angles, and vertical angles are equal.
$\angle NMP=\angle LMK = 48^{\circ}$

Answer:

$48$