Question

1. identify each pair of angles as corresponding, alternate interior, alternate exterior, same - side interior, vertical, or linear pair.

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position at each intersection where a straight - line crosses two others. Alternate interior angles are between the two lines and on opposite sides of the transversal. Alternate exterior angles are outside the two lines and on opposite sides of the transversal. Same - side interior angles are between the two lines and on the same side of the transversal. Vertical angles are opposite each other when two lines intersect. A linear pair is a pair of adjacent angles whose non - common sides are opposite rays.

Step2: Analyze the first diagram

For the first diagram with two parallel lines cut by a transversal, angles \(x\) and \(y\) are corresponding angles as they are in the same relative position at each intersection.

Step3: Analyze the second diagram

For the second diagram with two parallel lines cut by a transversal, angles \(x\) and \(y\) are alternate interior angles as they are between the two lines and on opposite sides of the transversal.

Answer:

First diagram: Corresponding angles
Second diagram: Alternate interior angles