If the smallest angle of rotation for a regular polygon is $18°$, how many sides does the polygon have?

• A. $10$
• B. $18$
• C. $20$
• D. $36$

Answer: (C)

Verified step by step guidance

1. Recall that the smallest angle of rotation for a regular polygon is the central angle of rotation that maps the polygon onto itself. This angle is given by the formula \(\theta = \frac{360^\circ}{n}\), where \(n\) is the number of sides of the polygon.
2. Given the smallest angle of rotation \(\theta = 18^\circ\), set up the equation \$18 = \frac{360}{n}\( to find the number of sides \)n$.
3. To solve for \(n\), multiply both sides of the equation by \(n\) to get \$18n = 360$.
4. Next, divide both sides by 18 to isolate \(n\): \(n = \frac{360}{18}\).
5. Simplify the fraction to find the number of sides \(n\) of the regular polygon.