Question

Through which angle of rotation does the image of a regular pentagon coincide with its preimage?

Answer 1

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 2

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

72°

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:

`(360)/(n)`

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:

`(360)/(5)=72`