What theorem can be used to prove the lines

Question

In the given figure x = 145°. What theorem can be used to prove the lines p and q are parallel?

Question 18 options:

	A)	Same side interior angles converse theorem
B)	Corresponding angles converse theorem
C)	Alternate interior angles converse theorem
D)	Alternate exterior angles converse theorem

Answer 1

The answer is D: The Alternate Exterior Angles Converse Theorem.

This Alternate Exterior Angles theorem explains that if a pair of parallel lines are cut by a transversal, then the alternate exterior angles are congruent. Therefore, the converse of said theorem would be if the two exterior angles are congruent, then the lines cut by the transversal must be parallel.

Because the diagram shows that the exterior angles are congruent (both equal x) then that therefore proves that the lines are parallel.

Hope that helps!