Theorem. Same-Side Interior Angles Theorem
If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary.

In the figure below, if $m\parallel n,$ then $\angle 4$ and $\angle 6$ are supplementary. The same is true of $\angle 3$ and $\angle 5.$ Prove the theorem using the first angle pair and the other pair can be proven similarly.