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

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.

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

The angle of rotation through which the image of a regular pentagon coincide with its preimage is:

          Option: B

            B.   72 degrees

Step-by-step explanation:

Rotational symmery–

Rotational symmetry is the minimum angle by which a figure is rotated such that it coincides with the original figure.

We know that for any n-regular polygon (i.e. a regular polygon with n number of sides) has a rotational symmetry of:

                    dfrac{360}{n} degrees

Here we are asked to find the rotational symmetry in case of pentagon i.e.  n=5

The angular symmetry is:

             dfrac{360}{5}=72 degrees

Step-by-step explanation:

e

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