Question

given the information in the diagram, which theorem best justifies why lines j and k must be parallel? alternate interior angles theorem alternate exterior angles theorem converse alternate interior angles theorem converse alternate exterior angles theorem

Explanation:

• Alternate exterior angles are angles that lie outside the two lines and on opposite sides of the transversal.
• The converse of a theorem is used to prove that two lines are parallel. Here, we are given the angles and need to prove lines \(j\) and \(k\) are parallel. Since the \(93^{\circ}\) angles are alternate exterior angles and they are equal, the converse of the alternate exterior angles theorem (which states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the two lines are parallel) is applicable.
• The alternate interior angles theorem and alternate exterior angles theorem are used to prove angle congruence when lines are parallel (not to prove lines are parallel). The converse alternate interior angles theorem would apply to angles inside the two lines, but here the angles are outside (exterior).

Answer:

converse alternate exterior angles theorem