Question

determine if (lparallel m). if yes, state the converse that proves the lines parallel
answer attempt 1 out of 100
not parallel
(lparallel m) by converse of alternate exterior angles
(lparallel m) by converse of same side exterior angles
(lparallel m) by converse of alternate interior angles
(lparallel m) by converse of same side interior angles
(lparallel m) by converse of corresponding angles

Explanation:

Step1: Analyze angle - sum

The two given angles are \(65^{\circ}\) and \(115^{\circ}\), and \(65 + 115=180^{\circ}\). These two angles are same - side interior angles.

Step2: Apply parallel - line converse

The converse of the same - side interior angles postulate states that if two lines are cut by a transversal and the same - side interior angles are supplementary (add up to \(180^{\circ}\)), then the two lines are parallel.

Answer:

\(l\parallel m\) by Converse of same side interior angles