Answer
(a) $210^{\circ}$
(b) $220^{\circ}$
Work Step by Step
(a) We can find the number of vertices of the polygon:
$30^{\circ} = \frac{360^{\circ}}{n}$
$n = \frac{360^{\circ}}{30^{\circ}}$
$n = 12$
We can find the interior angle of this polygon:
$\frac{(n-2)(180^{\circ})}{n} = \frac{(12-2)(180^{\circ})}{12} = 150^{\circ}$
We can find the exterior angle of this polygon:
$360^{\circ} - 150^{\circ} = 210^{\circ}$
(b) We can find the number of vertices of the polygon:
$40^{\circ} = \frac{360^{\circ}}{n}$
$n = \frac{360^{\circ}}{40^{\circ}}$
$n = 9$
We can find the interior angle of this polygon:
$\frac{(n-2)(180^{\circ})}{n} = \frac{(9-2)(180^{\circ})}{9} = 140^{\circ}$
We can find the exterior angle of this polygon:
$360^{\circ} - 140^{\circ} = 220^{\circ}$
