Answer
$\overline{PL}$must be parallel to $\overline{NA}$, and $\overline{PN}$ must be parallel to $\overline{LA}$.
Work Step by Step
If the same-side interior angles are supplementary, then the lines must be parallel by the Converse of the Same Side Interior Angles Theorem, which states: If two lines are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel.
