Question

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

Answer 1

Its 72 degrees i just did this one plato 

Answer 2

Answer-

When rotated a angle of 72°, a regular pentagon coincides with its pre-image.

Solution-

A polygon is regular when all angles are equal and all sides are equal. So, when a pentagon's all 5 angles and sides are equal then it's called as a regular pentagon.

The angel subtended by two consecutive radius of a regular pentagon(i.e the line joining vertices and the center of the pentagon) at the center is 72°.

Due to its symmetry when a regular pentagon is rotated 72° around its center(both clockwise and counter-clockwise), it produces same pentagon as before.