lines m and n are cut by transversal l. which angle relationships are correct? check all that apply. ∠1 and…

Explanation:

Step1: Recall angle - relationship definitions

Alternate exterior angles are outside the two lines and on opposite sides of the transversal. ∠1 and ∠8 are outside lines m and n and on opposite sides of l, so they are alternate exterior angles.

Step2: Recall same - side interior angles

Same - side interior angles are between the two lines and on the same side of the transversal. ∠4 and ∠6 are between m and n and on the same side of l, so they are same - side interior angles.

Step3: Recall vertical angles

Vertical angles are opposite each other at an intersection. ∠5 and ∠7 are opposite each other at the intersection of l and n, so they are vertical angles.

Step4: Recall corresponding angles

Corresponding angles are in the same relative position with respect to the lines and the transversal. ∠2 and ∠8 are not in corresponding positions.

Step5: Recall alternate interior angles

Alternate interior angles are between the two lines and on opposite sides of the transversal. ∠3 and ∠6 are between m and n and on opposite sides of l, so they are alternate interior angles.

Answer:

∠1 and ∠8 are alternate exterior angles. ∠4 and ∠6 are same side interior angles. ∠5 and ∠7 are vertical angles. ∠3 and ∠6 are alternate interior angles.