Chapter 3 - Parallel and Perpendicular Lines - 3-2 Properties of Parallel Lines - Practice and Problem-Solving Exercises: 23

$m\angle1=117$ 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

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