Question

∠1 and ∠5 are vertical angles, ∠5 and ∠6 are supplementary angles, and m∠6 = 110.2°. what is m∠1, in degrees?

Explanation:

Step1: Find measure of ∠5

Supplementary angles sum to 180°. So $m\angle5=180 - m\angle6$.
$m\angle5 = 180 - 110.2=69.8^{\circ}$

Step2: Find measure of ∠1

Vertical angles are equal. Since ∠1 and ∠5 are vertical angles, $m\angle1=m\angle5$.
$m\angle1 = 69.8^{\circ}$

Answer:

$69.8$