Question

given the following information, determine which lines, if any, are parallel 15. state the converse that justifies your answer. parallel lines: l and n, converse: consecutive interior converse parallel lines: l and n, converse: linear pair converse parallel lines: l and n, converse: alternate exterior angles converse m∠7 + m∠19 = 180°

Explanation:

Step1: Recall the consecutive interior angles converse

If two lines are cut by a transversal and the consecutive interior angles are supplementary, then the two lines are parallel.

Step2: Analyze the given angles

Here, \(\angle7\) and \(\angle19\) are consecutive interior angles (they lie between the two lines \(l\) and \(n\) and on the same side of the transversal \(k\)). Given that \(m\angle7 + m\angle19=180^{\circ}\) (they are supplementary).

Step3: Apply the converse

By the consecutive interior angles converse, lines \(l\) and \(n\) are parallel.

Answer:

parallel lines: \(l\) and \(n\), converse: consecutive interior converse