Question

given ( mangle 3 + mangle 7 = 180^circ ), determine which lines, if any, are parallel. state the converse that justifies your ar
parallel lines: ( lparallel m )
converse: consecutive (same - side) <

Explanation:

Step1: Identify the relationship between ∠3 and ∠7

∠3 and ∠7 are consecutive (same - side) interior angles formed by lines \( l \) and \( m \) with a transversal.

Step2: Apply the converse of the consecutive interior angles theorem

The converse of the consecutive interior angles theorem states that if two lines are cut by a transversal and the consecutive interior angles are supplementary (\(m\angle3 + m\angle7=180^{\circ}\)), then the two lines are parallel.

Answer:

Lines \( l \) and \( m \) are parallel. The converse that justifies this is the converse of the consecutive (same - side) interior angles theorem.