Question

tell the relationship between the pairs of angles based on the diagram below. angles 1 and 3 are vertical. angles 2 and 7 are . angles 4 and 5 are . angles 2 and 8 are . alternate interior alternate exterior same side interior same side exterior

Explanation:

Step1: Recall angle - pair relationships

When two parallel lines are cut by a transversal, different types of angle - pairs are formed.

Step2: Analyze angles 2 and 7

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

Step3: Analyze angles 4 and 5

Angles 4 and 5 are same - side interior angles as they are on the inside of the two parallel lines and on the same side of the transversal.

Step4: Analyze angles 2 and 8

Angles 2 and 8 are corresponding angles as they are in the same relative position with respect to the parallel lines and the transversal.

Answer:

Angles 2 and 7 are alternate exterior.
Angles 4 and 5 are same - side interior.
Angles 2 and 8 are corresponding.