Question

1. find m∠1 and m∠2. tell which theorem you would use in each case.

2.

Explanation:

Step1: Identify angle - relationships

$\angle1$ and the $117^{\circ}$ angle are vertical angles.

Step2: Apply vertical - angles theorem

Vertical angles are congruent. So $m\angle1 = 117^{\circ}$.

Step3: Identify another angle - relationship

$\angle2$ and the $117^{\circ}$ angle are corresponding angles.

Step4: Apply corresponding - angles theorem

When two parallel lines are cut by a transversal, corresponding angles are congruent. So $m\angle2 = 117^{\circ}$.

Answer:

$m\angle1 = 117^{\circ}$, $m\angle2=117^{\circ}$