Question

a regular pentagon is shown below. suppose that the pentagon is rotated clockwise about its center so that the vertex at c is moved to e. how many degrees does the pentagon rotate?

Explanation:

Step1: Find central - angle of pentagon

The central - angle of a regular pentagon is calculated by $\frac{360^{\circ}}{n}$, where $n = 5$ (number of sides). So, $\frac{360^{\circ}}{5}=72^{\circ}$.

Step2: Determine number of vertices between C and E

Counting clock - wise from C to E, there are 2 vertices between them.

Step3: Calculate rotation angle

The rotation angle $\theta$ is the product of the central - angle and the number of vertices between C and E. So, $\theta=72^{\circ}\times2 = 144^{\circ}$.

Answer:

$144^{\circ}$