Answer
(a) $140^{\circ}$
(b) $135^{\circ}$
Work Step by Step
(a) 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:
$\frac{(n-2)(180^{\circ})}{n} = \frac{(9-2)(180^{\circ})}{9} = 140^{\circ}$
(b) 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:
$\frac{(n-2)(180^{\circ})}{n} = \frac{(8-2)(180^{\circ})}{8} = 135^{\circ}$
