Question

angles 2 and 7 are
angles 4 and 5 are
angles 2 and 8 are
angles 1 and 3 are

find the relationship between the pairs of angles based on the diagram below.

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. Alternate exterior angles are non - adjacent angles that lie outside 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. Same - side interior angles are two angles that lie between 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. Corresponding angles are in the same relative position with respect to the parallel lines and the transversal.

Step5: Analyze angles 1 and 3

Angles 1 and 3 are vertical angles. Vertical angles are opposite angles formed by the intersection of two lines.

Answer:

Angles 2 and 7 are alternate exterior angles.
Angles 4 and 5 are same - side interior angles.
Angles 2 and 8 are corresponding angles.
Angles 1 and 3 are vertical angles.