Given that r || s and q is a transversal, we know that
∠3 ≅ ∠6 by the . Therefore, m∠3 = m∠6 by the definition of congruent. We also know that, by definition, ∠4 and ∠3 are a linear pair, so they are supplementary by the linear pair postulate. By the definition of supplementary angles, m∠4 + m∠3 = 180°. Using substitution, we can replace m∠3 with m∠6 to get m∠4 + m∠6 = 180°. Therefore, by the definition of supplementary angles, ∠4 is supplementary to ∠6.
ANSWER CHOICES:
A) Corresponding angles theorem
B) Alternate interior angles theorem
C) Vertical angles theorem
D) Alternate exterior angles theorem