Question

use the image shown above to determine the relationship between each pair of angles listed below. select the correct option for each pair of angles
angles alternate interior alternate exterior corresponding same - side interior vertical
2 and 7
1 and 8
4 and 5

Explanation:

Step1: Recall angle - pair definitions

Alternate interior angles are between the two parallel lines and on opposite sides of the transversal. Alternate exterior angles are outside the two parallel lines and on opposite sides of the transversal. Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. Same - side interior angles are between the two parallel lines and on the same side of the transversal. Vertical angles are opposite each other when two lines intersect.

Step2: Analyze ∠2 and ∠7

∠2 and ∠7 are outside the two parallel lines and on opposite sides of the transversal. So they are alternate exterior angles.

Step3: Analyze ∠1 and ∠8

∠1 and ∠8 are outside the two parallel lines and on opposite sides of the transversal. So they are alternate exterior angles.

Step4: Analyze ∠4 and ∠5

∠4 and ∠5 are between the two parallel lines and on opposite sides of the transversal. So they are alternate interior angles.

Answer:

Angles	Alternate Interior	Alternate Exterior	Corresponding	Same - Side Interior	Vertical
1 and 8		X
4 and 5	X