Question

Lines e and f are intersected by line a. At the intersection of lines a and e, the bottom right angle is 72 degrees. At the intersection of lines a and f, the uppercase right angle is 108 degrees.
Given the information in the diagram, which theorem best justifies why lines e and f must be parallel?

alternate interior angles theorem
same side interior angles theorem
converse of the alternate interior angles theorem
converse of the same side interior angles theorem

Answer 1

converse of the same side interior angles theorem

Reason: the given angles (72° and 108°) are same-side interior angles formed by transversal a, and they are supplementary (72° + 108° = 180°). By the converse of the same-side interior angles theorem, the lines e and f are parallel.