In the diagram below, two lines are intersected by a transversal. Let angle $1$, angle $2$, angle $3$, and angle $4$ denote the angles formed at the intersection. If angle $1$ measures $x$ degrees and angle $3$ is vertically opposite angle $1$, what is the measure of angle $4$ if it is supplementary to angle $2$?
Given that angles that are vertically opposite are equal, and supplementary angles add up to $180$ degrees.