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: Recall supplementary - angle property

Supplementary angles add up to 180°. Given $\angle5$ and $\angle6$ are supplementary and $m\angle6 = 110^{\circ}$, we have $m\angle5+m\angle6=180^{\circ}$. So $m\angle5=180 - m\angle6$.
$m\angle5=180 - 110=70^{\circ}$

Step2: Recall vertical - angle property

Vertical angles are equal. Since $\angle1$ and $\angle5$ are vertical angles, $m\angle1 = m\angle5$.
$m\angle1=70^{\circ}$

Answer:

$70$