Question

1. give a list of all rotations of symmetry between 0° and 360°. separate your answers with commas and no spaces. regular pentagon

Explanation:

Step1: Recall rotation - symmetry formula

For a regular \(n\) - sided polygon, the angles of rotation of symmetry are given by \(\theta=\frac{360^{\circ}k}{n}\), where \(k = 0,1,\cdots,n - 1\) and \(n\) is the number of sides of the polygon. Here, \(n = 5\) (a pentagon).

Step2: Calculate rotation angles

When \(k = 0\), \(\theta=\frac{360\times0}{5}=0^{\circ}\) (not in our non - zero range).
When \(k = 1\), \(\theta=\frac{360\times1}{5}=72^{\circ}\).
When \(k = 2\), \(\theta=\frac{360\times2}{5}=144^{\circ}\).
When \(k = 3\), \(\theta=\frac{360\times3}{5}=216^{\circ}\).
When \(k = 4\), \(\theta=\frac{360\times4}{5}=288^{\circ}\).

Answer:

72,144,216,288