Question

1. find the m∠1. name the angle pair used.
2. find the m∠1. name the angle pair used.
3. find the m∠1. name the angle pair used.
4. find the value of x. name the angle pair used.
5. find the value of x. name the angle pair used.
6. find the value of x. name the angle pair used.

Explanation:

1.

Step1: Identify angle - pair type

The angles are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.
So \(m\angle1 = 74^{\circ}\)

Step1: Identify angle - pair type

The angles are alternate - exterior angles. Alternate - exterior angles are equal when two parallel lines are cut by a transversal.
So \(m\angle1 = 81^{\circ}\)

Step1: Identify angle - pair type

The angles are corresponding angles. Since corresponding angles are equal when two parallel lines are cut by a transversal, \(m\angle1=87^{\circ}\)

Answer:

\(m\angle1=74^{\circ}\), Corresponding angles

2.