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

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:

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:

last option: rhombus or kite

step-by-step explanation:

a kite and rhombus have the same shape. as we don't have any specific formula for the calculation of area of kite. the diagonals are used to calculate the area of a kite or rhombus.

the formula for area of rhombus is given by:

here, d_1 is the first diagonal and d_2 is the second diagonal.

so,

last option is the correct answer ..