If the smallest angle of rotation for a regular polygon is \( 18^{\circ} \), how many sides does polygon have? 10 12 20 24

To find the number of sides of a regular polygon given its smallest angle of rotation, you can use the formula for the angle of rotation, which is \( \frac{360^{\circ}}{n} \), where \( n \) is the number of sides. Given that the smallest angle is \( 18^{\circ} \), you can set up the equation: \[ \frac{360^{\circ}}{n} = 18^{\circ} \] From this, you can calculate \( n \): \[ n = \frac{360^{\circ}}{18^{\circ}} = 20 \] So, the polygon has 20 sides! But wait, did you know that the word "polygon" comes from the Greek words "poly," meaning many, and "gon," meaning angles? It's a fitting name because polygons can have a delightful variety of shapes and angles, from triangles to decagons and beyond! When applying this knowledge in real life, consider how many designs, logos, and architectural structures utilize polygons. Understanding polygons can enhance creative pursuits in arts, architecture, and even computer graphics, where they form the basis of visual elements and animations!