Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $b$ and the $80^{\circ}$ angle are vertical angles, so $b = 80^{\circ}$.

Step2: Use supplementary - angle property

Angles $b$ and $c$ are supplementary (a linear - pair), so $b + c=180^{\circ}$. Substitute $b = 80^{\circ}$ into the equation: $80^{\circ}+c = 180^{\circ}$, then $c=180^{\circ}-80^{\circ}=100^{\circ}$.

Answer:

$b = 80^{\circ}$, $c = 100^{\circ}$