Question

identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutive interior, or vertical.
1)
2)
3)
4)
5)
6)
find the measure of each angle indicated.
7)
8)

Explanation:

Step1: Recall angle - pair definitions

Corresponding angles are in the same relative position, alternate interior angles are between the parallel lines and on opposite sides of the transversal, alternate exterior angles are outside the parallel lines and on opposite sides of the transversal, consecutive interior angles are between the parallel lines and on the same side of the transversal, and vertical angles are opposite each other when two lines intersect.

Step2: Identify angle - pairs for 1 - 6

1. Corresponding angles: Angles \(x\) and \(y\) are in the same relative position with respect to the parallel lines and the transversal.
2. Alternate interior angles: Angles \(x\) and \(y\) are between the parallel lines and on opposite sides of the transversal.
3. Alternate exterior angles: Angles \(x\) and \(y\) are outside the parallel lines and on opposite sides of the transversal.
4. Consecutive interior angles: Angles \(x\) and \(y\) are between the parallel lines and on the same side of the transversal.
5. Vertical angles: Angles \(x\) and \(y\) are opposite each other when two lines intersect.
6. Corresponding angles: Angles \(x\) and \(y\) are in the same relative position with respect to the parallel lines and the transversal.

Step3: Recall angle - measure relationships for 7 - 8

For parallel lines cut by a transversal, corresponding angles are congruent, vertical angles are congruent.

1. The angle indicated is vertical to the \(95^{\circ}\) angle. Since vertical angles are congruent, the measure of the indicated angle is \(95^{\circ}\).
2. The angle indicated is corresponding to the \(99^{\circ}\) angle. Since corresponding angles are congruent, the measure of the indicated angle is \(99^{\circ}\).

Answer:

1. Corresponding
2. Alternate interior
3. Alternate exterior
4. Consecutive interior
5. Vertical
6. Corresponding
7. \(95^{\circ}\)
8. \(99^{\circ}\)