Question

a regular 18 - sided polygon is rotated with the center of rotation at its center. what is the smallest degree of rotation needed to map the polygon back on to itself?

Explanation:

Step1: Recall the formula for rotational symmetry

The formula for the smallest degree of rotation \( \theta\) for a regular \(n -\)sided polygon is \( \theta=\frac{360^{\circ}}{n}\).

Step2: Substitute \(n = 18\) into the formula

When \(n = 18\), we have \( \theta=\frac{360^{\circ}}{18}\).

$$ \theta = 20^{\circ} $$

Answer:

\(20^{\circ}\)