Answer :

since a complete turn would be of 360 and that a pentagon has 5 sides you take 360/5 =72 so each angle of 72 degrees returns the original configuration

Answer:

The angle of rotation by which the image of a regular pentagon coincide with its pre-image is:

                                        72°

Step-by-step explanation:

Regular polygon--

A regular polygon is a polygon in which all the sides and all the interior angles are equal i.e. the polygon is equilateral and equiangular.

In general the angle of rotation of a regular n-polygon is given by:

                    [tex]\dfrac{360}{n}[/tex]

where n is the number of sides in a polygon.

Here we have n=5 (pentagon)

Hence, the angle of rotation of the image is:

               [tex]\dfrac{360}{5}=72[/tex]