Question

find m∠1 and m∠2 given that lines n and m are parallel. justify your answer. m∠1 = ° by the

Explanation:

Step1: Identify angle - relationship

$\angle1$ and the $58^{\circ}$ angle are corresponding angles.

Step2: Use parallel - line property

Since lines $n$ and $m$ are parallel, corresponding angles are congruent. So $m\angle1 = 58^{\circ}$.

Step3: Find $m\angle2$

$\angle2$ and the $58^{\circ}$ angle are alternate - interior angles. Since lines $n$ and $m$ are parallel, alternate - interior angles are congruent. So $m\angle2=58^{\circ}$.

Answer:

$m\angle1 = 58^{\circ}$ by the corresponding - angles postulate.
$m\angle2 = 58^{\circ}$ by the alternate - interior angles theorem.