Question

two workers paint lines for angled parking spaces. one worker paints a line so that m∠1 = 64. the other worker paints a line so that m∠3 = 64. are their lines parallel? explain. are lines h and k parallel? yes, ∠3 and ∠1 are alternate exterior angles, and if alternate exterior angles are congruent, then the lines h and k are parallel. no, ∠3 and ∠1 are not alternate exterior angles, then the lines h and k are not parallel.

Explanation:

Step1: Recall angle - parallel line relationship

If two lines are cut by a transversal, alternate exterior angles are congruent when the lines are parallel.

Step2: Identify angle - pair type

Given that $\angle1$ and $\angle3$ are alternate exterior angles, and $m\angle1 = 64^{\circ}$, $m\angle3=64^{\circ}$.

Step3: Apply parallel - line theorem

Since alternate exterior angles $\angle1$ and $\angle3$ are congruent, by the converse of the alternate - exterior - angles theorem, lines $h$ and $k$ are parallel.

Answer:

Yes, lines $h$ and $k$ are parallel because $\angle3$ and $\angle1$ are alternate exterior angles, and since alternate exterior angles are congruent, the lines $h$ and $k$ are parallel.