Is the choice vertical angle theorem correct?

Unfortunately it is incorrect. You should instead go for the Alternate Exterior Angle Theorem

Angle 2 and angle 7 are on opposite or alternate sides of the transversal cut. They are also exterior because they are on the outside of the train tracks (think of line a and line b as the metal rail of the train tracks). If a || b, then the alternate exterior angles are congruent, which applies to angle 2 and angle 7. Also it applies to angle 1 and angle 8.