Question

which theorem correctly justifies why the lines m and n are parallel when cut by transversal k?
converse of the corresponding angles theorem
converse of the alternate interior angles theorem
converse of the same side interior angles theorem
converse of the alternate exterior angles theorem

Explanation:

To determine the theorem justifying lines \( m \) and \( n \) being parallel, we analyze the angles formed by transversal \( k \). The two \( 50^\circ \) angles are corresponding angles (in the same position relative to the parallel lines and transversal). The converse of the corresponding angles theorem states that if corresponding angles are congruent, then the lines are parallel. The other theorems (alternate interior, same - side interior, alternate exterior) do not apply here as the angles are not in the positions defined by those theorems.

Answer:

A. converse of the corresponding angles theorem