Question

find the measure of the missing angles. 31° b c

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $b$ and the $31^{\circ}$ angle are vertical angles, so $b = 31^{\circ}$.

Step2: Use linear - pair property

Angles $b$ and $c$ form a linear pair (a straight - line angle which is $180^{\circ}$). So $c=180^{\circ}-b$.
Substitute $b = 31^{\circ}$ into the equation: $c = 180^{\circ}-31^{\circ}=149^{\circ}$.

Answer:

$b = 31^{\circ}$, $c = 149^{\circ}$