Question

two workers paint lines for angled parking spaces. one worker paints a line so that m ∠2 = 64. the other worker paints a line so that m ∠3 = 64. are their lines parallel? explain. are lines g and h parallel? no; ∠2 and ∠3 are not alternate exterior angles, then the lines g and h are not parallel. yes; ∠2 and ∠3 are alternate exterior angles, and if alternate exterior angles are congruent, then the lines g and h are parallel

Explanation:

Step1: Recall parallel - line theorem

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

Step2: Identify angle relationship

$\angle2$ and $\angle3$ are alternate exterior angles and $m\angle2 = 64$ and $m\angle3=64$, so $\angle2\cong\angle3$.

Answer:

Yes; $\angle2$ and $\angle3$ are alternate exterior angles, and if alternate exterior angles are congruent, then the lines g and h are parallel.