Question

using parallel lines find m∠1 and m∠2. explain your reasoning. 9.

Explanation:

Step1: Identify vertical - angle relationship

$\angle1$ and the $82^{\circ}$ angle are vertical angles. Vertical angles are congruent.
So, $m\angle1 = 82^{\circ}$

Step2: Identify linear - pair relationship

$\angle1$ and $\angle2$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$.
Since $m\angle1 = 82^{\circ}$, then $m\angle2=180^{\circ}-m\angle1 = 180 - 82=98^{\circ}$

Answer:

$m\angle1 = 82^{\circ}$, $m\angle2 = 98^{\circ}$