Question

using parallel lines find m∠1 and m∠2. explain your reasoning. 10. 118° 1 2

Explanation:

Step1: Identify angle - relationship

The 118 - degree angle and ∠1 are vertical angles.
Since vertical angles are congruent, $m\angle1 = 118^{\circ}$.

Step2: Find m∠2

∠1 and ∠2 are supplementary angles (linear - pair).
The sum of angles in a linear - pair is 180°. So $m\angle2=180 - m\angle1$.
Substitute $m\angle1 = 118^{\circ}$ into the formula: $m\angle2=180 - 118=62^{\circ}$.

Answer:

$m\angle1 = 118^{\circ}$, $m\angle2 = 62^{\circ}$