Question

using parallel lines find ( mangle1 ) and ( mangle2 ). explain your reasoning. (review 3.3 for 4.4) 41.

Explanation:

Step1: Find \( m\angle2 \)

Vertical angles are equal. So \( m\angle2 = 57^{\circ} \)

Step2: Find \( m\angle1 \)

\(\angle1\) and \(\angle2\) are supplementary (consecutive interior angles). So \( m\angle1=180^{\circ}-m\angle2 \)
Substitute \( m\angle2 = 57^{\circ} \) into the formula: \( m\angle1 = 180^{\circ}-57^{\circ}=123^{\circ} \)

Answer:

\( m\angle1 = 123^{\circ} \), \( m\angle2 = 57^{\circ} \)