The angle created by a hinged mirror when forming a regular polygon is called a central angle. For example, $∠ABC$ in the diagram below is the central angle of the regular hexagon. Homework Help ✎

1. If the central angle of a regular polygon measures $18°$, how many sides does the polygon have?

   Step 1(a):

   $\text{number}\ \text{of}\ \text{sides}=\frac{360}{18}$

2. Can a central angle measure $90°$? $180°$? $13°$? For each angle measure, explain how you know.

   Hint (b):

   Try drawing shapes that could have the central angle measurements that have been listed.