Question

1. which theorem would be used to write 15x + 12 + 117 = 180 in the diagram below?

vertical angles theorem
alternate interior angles theorem
consecutive exterior angles theorem
corresponding angles theorem

Explanation:

Step1: Identify angle - pair relationship

The angles \(15x + 12\) and \(117^{\circ}\) are consecutive exterior angles formed by two parallel lines \(k\) and \(j\) and a transversal \(l\).

Step2: Recall angle - theorem

Consecutive exterior angles are supplementary (add up to \(180^{\circ}\)) when the lines are parallel.

Answer:

C. Consecutive Exterior Angles Theorem