Question

find ( mangle 1 ), ( mangle 2 ) and ( mangle 3 ). explain your reasoning.
( mangle 1=) by the
( mangle 3=) by the
( mangle 2=) by the

Explanation:

Step1: Find \(m\angle1\)

Since \(\angle1\) and the \(80^{\circ}\) angle are alternate interior angles, \(m\angle1 = 80^{\circ}\) (Alternate Interior Angles Theorem).

Step2: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are vertical angles. Vertical angles are congruent. So \(m\angle2=m\angle1 = 80^{\circ}\) (Vertical Angles Theorem).

Step3: Find \(m\angle3\)

\(\angle3\) and the \(80^{\circ}\) angle are supplementary (they form a linear pair). So \(m\angle3=180^{\circ}- 80^{\circ}=100^{\circ}\) (Linear Pair Postulate).

Answer:

\(m\angle1 = 80^{\circ}\) (by the Alternate Interior Angles Theorem), \(m\angle2 = 80^{\circ}\) (by the Vertical Angles Theorem), \(m\angle3 = 100^{\circ}\) (by the Linear Pair Postulate)