1. **Problem statement:** Given two parallel lines $\overline{LN}$ and $\overline{OQ}$, and a transversal intersecting them at points $M$ and $P$ respectively, with $m \angle LMK = 113^\circ$, find $m \angle QPM$. 2. **Key concept:** When a transversal crosses parallel lines, alternate interior angles are equal. 3. **Identify angles:** $\angle LMK$ and $\angle QPM$ are alternate interior angles because $\overline{LN} \parallel \overline{OQ}$ and $\overline{MKP}$ is the transversal. 4. **Apply the rule:** Since alternate interior angles are equal, $$m \angle QPM = m \angle LMK = 113^\circ$$ 5. **Final answer:** $$m \angle QPM = 113^\circ$$