Answer
$m\angle1=117$
same-side interior
Work Step by Step
The rope represents the transversal, and the trees represent the parallel lines.
The two labeled angles are same-side interior angles because they are on the same side of the rope (transvesal) and between the trees (lines).
The same-side interior angle postulate tells us the two angles are supplementary.
$m\angle1+63=180\longrightarrow$ definition of supplementary
$m\angle1=117\longrightarrow$ subtraction property of equality
