Geometry: Common Core (15th Edition)

The Converse of the Same-Side Interior Angles Postulate tells us the lines are parallel when the same-side interior angles are supplementary. The vertical angle to the angle marked $105^o$ and the angle marked $3x-18$ are same-side interior angles. $(3x-18)+105=180\longrightarrow$ definition of supplementary $3x+87=180\longrightarrow$ simplification $3x=93\longrightarrow$ subtraction property of equality $x=31\longrightarrow$ division property of equality