Question

if the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have? 10 12 20 24

Explanation:

Step1: Recall the formula for the smallest rotation angle

The smallest angle of rotation for a regular polygon is given by \(\frac{360^{\circ}}{n}\), where \(n\) is the number of sides.

Step2: Set up the equation

We know that \(\frac{360^{\circ}}{n}=18^{\circ}\).

Step3: Solve for \(n\)

Cross - multiply: \(n=\frac{360^{\circ}}{18^{\circ}}\).
Calculate: \(n = 20\).

Answer:

C. 20