Question

use the figure on the right to answer #8

1. find ( mangle1,mangle2 ), and ( mangle3 ). explain your reasoning.

(reasoning options are types of angle pairs)
( mangle1=)
( mangle1 ) reasoning:
( mangle2=)
( mangle2 ) reasoning:
( mangle3=)
( mangle3 ) reasoning:

Explanation:

Step1: Find \(m\angle1\)

\(\angle1\) and the \(57^{\circ}\) angle are vertical angles. Vertical angles are equal. So \(m\angle1=57^{\circ}\)

Step2: Find \(m\angle2\)

The \(57^{\circ}\) angle and \(\angle2\) are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are equal. So \(m\angle2 = 57^{\circ}\)

Step3: Find \(m\angle3\)

\(\angle3\) and the \(57^{\circ}\) angle are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are equal. So \(m\angle3=57^{\circ}\)

Answer:

\(m\angle1 = 57^{\circ}\), \(m\angle2 = 57^{\circ}\), \(m\angle3 = 57^{\circ}\)