Answer
(a) $120^{\circ}$
(b) $90^{\circ}$
Work Step by Step
(a) We can find the number of vertices of the polygon:
$60^{\circ} = \frac{360^{\circ}}{n}$
$n = \frac{360^{\circ}}{60^{\circ}}$
$n = 6$
We can find the interior angle of this polygon:
$\frac{(n-2)(180^{\circ})}{n} = \frac{(6-2)(180^{\circ})}{6} = 120^{\circ}$
(b) We can find the number of vertices of the polygon:
$90^{\circ} = \frac{360^{\circ}}{n}$
$n = \frac{360^{\circ}}{90^{\circ}}$
$n = 4$
We can find the interior angle of this polygon:
$\frac{(n-2)(180^{\circ})}{n} = \frac{(4-2)(180^{\circ})}{4} = 90^{\circ}$
