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 $80^{\circ}$ angle are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent.

Step2: Find $m\angle1$

$m\angle1 = 80^{\circ}$ (Corresponding angles postulate)

Step3: Identify angle - relationship for $\angle2$

$\angle2$ and the $80^{\circ}$ angle are alternate interior angles. When two parallel lines are cut by a transversal, alternate interior angles are congruent.

Step4: Find $m\angle2$

$m\angle2=80^{\circ}$ (Alternate interior angles theorem)

Answer:

$m\angle1 = 80^{\circ}$ by the Corresponding angles postulate; $m\angle2 = 80^{\circ}$ by the Alternate interior angles theorem