Question

two workers paint lines for angled parking spaces. one worker paints a line so that m∠1 = 67. the other worker paints a line so that m∠2 = 67. are their lines parallel? explain. are lines k and n parallel? yes, ∠1 and ∠2 are alternate exterior angles, and if alternate exterior angles are congruent, then the lines k and n are parallel. no, ∠1 and ∠2 are not alternate exterior angles, then the lines k and n are not parallel.

Explanation:

Step1: Recall parallel - line theorem

If alternate exterior angles are congruent, then the two lines are parallel.

Step2: Analyze given angles

We are given that \(\angle1 = 67^{\circ}\) and \(\angle2=67^{\circ}\). Since \(\angle1\) and \(\angle2\) are alternate exterior angles and \(\angle1=\angle2 = 67^{\circ}\), they are congruent.

Answer:

Yes, lines \(k\) and \(n\) are parallel.