∠3 is congruent to ∠2 because of the vertical angles theorem. This theorem states vertical angles (angles opposite each other) are congruent.
∠6 is congruent to ∠2 because of the corresponding angles theorem. This theorem states corresponding angles (angles that are in the same position as their correspondent) are congruent.
∠7 is congruent to ∠2 because of the alternate exterior angles theorem. This theorem states that alternate exterior angles (angles on opposite sides of the transversal and outside the two parallel lines) are congruent.
