Question

use the regular pentagon shown.
what is the least angle of rotation in degrees that maps the pentagon onto itself?

Explanation:

Step1: Recall the formula for rotation angle of a regular polygon

The formula for the least - angle of rotation \(\theta\) that maps a regular \(n\) - sided polygon onto itself is \(\theta=\frac{360^{\circ}}{n}\), where \(n\) is the number of sides of the polygon.

Step2: Identify the number of sides of the pentagon

For a pentagon, \(n = 5\).

Step3: Calculate the rotation angle

Substitute \(n = 5\) into the formula \(\theta=\frac{360^{\circ}}{n}\). So, \(\theta=\frac{360^{\circ}}{5}=72^{\circ}\)

Answer:

\(72\)