Question

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$b=square^{circ}$ $c=square^{circ}$
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Explanation:

Step1: Identify vertical - angle relationship

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

Step2: Determine the value of $b$

Since vertical angles are equal, $b = 31^{\circ}$.

Step3: Identify supplementary - angle relationship

Angle $c$ and the $31^{\circ}$ angle are supplementary (they form a straight - line). The sum of supplementary angles is $180^{\circ}$.

Step4: Calculate the value of $c$

$c=180^{\circ}-31^{\circ}=149^{\circ}$

Answer:

$b = 31$
$c = 149$