Through which angle of rotation does the image of a regular pentagon coincide with its preimage?
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
The angle of rotation by which the image of a regular pentagon coincide with its pre-image is:
72°
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:
\(\dfrac{360}{n}\)
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:
\(\dfrac{360}{5}=72\)