Question

6
type the correct answer in the box. use numerals instead of words.
the regular pentagon abcde rotates counterclockwise about its center to form pentagon abcde
the angle of rotation at which point a coincides with point d is

Explanation:

Step1: Calculate the central angle of a regular pentagon

The formula for the central angle of a regular \(n -\)sided polygon is \(\theta=\frac{360^{\circ}}{n}\). For a pentagon, \(n = 5\), so \(\theta=\frac{360^{\circ}}{5}=72^{\circ}\).

Step2: Determine the number of intervals from \(A\) to \(D\)

Counting the number of intervals (vertices) from \(A\) to \(D\) in a counter - clockwise direction. The number of intervals \(k = 3\).

Step3: Calculate the rotation angle

The rotation angle \(\alpha=k\times\theta\). Substitute \(k = 3\) and \(\theta = 72^{\circ}\), we get \(\alpha=3\times72^{\circ}=216^{\circ}\).

Answer:

216