Question

1. write a two - column proof for exercise proof find m∠1 and m∠2. justify each answer. 12. 13.

Explanation:

Step1: Identify angle - relationship

Since lines $\ell$ and $m$ are parallel and $t$ is a transversal, $\angle1$ and the $75^{\circ}$ angle are corresponding angles.

Step2: Find $m\angle1$

Corresponding angles are congruent when two parallel lines are cut by a transversal. So $m\angle1 = 75^{\circ}$.

Step3: Identify another angle - relationship

$\angle1$ and $\angle2$ are vertical angles.

Step4: Find $m\angle2$

Vertical angles are congruent. Since $m\angle1 = 75^{\circ}$, then $m\angle2=75^{\circ}$.

Answer:

$m\angle1 = 75^{\circ}$, $m\angle2 = 75^{\circ}$