Answer
(a) $225^{\circ}$
(b) $300^{\circ}$
Work Step by Step
(a) We can find the number of vertices of the polygon:
$45^{\circ} = \frac{360^{\circ}}{n}$
$n = \frac{360^{\circ}}{45^{\circ}}$
$n = 8$
We can find the interior angle of this polygon:
$\frac{(n-2)(180^{\circ})}{n} = \frac{(8-2)(180^{\circ})}{8} = 135^{\circ}$
We can find the exterior angle of this polygon:
$360^{\circ} - 135^{\circ} = 225^{\circ}$
(b) We can find the number of vertices of the polygon:
$120^{\circ} = \frac{360^{\circ}}{n}$
$n = \frac{360^{\circ}}{120^{\circ}}$
$n = 3$
We can find the interior angle of this polygon:
$\frac{(n-2)(180^{\circ})}{n} = \frac{(3-2)(180^{\circ})}{3} = 60^{\circ}$
We can find the exterior angle of this polygon:
$360^{\circ} - 60^{\circ} = 300^{\circ}$
