Question

If a regular polygon has 20 degree rotational symmetry, how many sides does it have?

Answer 1

Hint: In the given question, we have been asked to find the number of sides of a regular polygon that has a 20 degree rotational symmetry. In order to find the number of sides, we only need to divide the whole degree of rotational symmetry that is equal to 360 degree by the degree of rotational symmetry of a regular polygon.

Complete step-by-step solution:
We have given that,
A regular polygon has 20 degree rotational symmetry.
Here,
As we know that the total symmetry is 360 degrees or we can say that the rotational symmetry always adds up to 360 degrees.
To find the number of sides of a regular polygon, we need to divide the whole degree of rotational symmetry that is equal to 360 degree by the degree of rotational symmetry of a given polygon.
Therefore,
Number of sides of a regular polygon = $${\displaystyle \frac{360}{20}}=18$$
Therefore, the total number of sides of a regular polygon is 18.

Therefore a regular polygon of 18 sides has 20 degree rotational symmetry.

Note: The important point that students need to remember here is that the rotational symmetry’s degree will always add up to 360 degree. They need to know that a regular polygon is a polygon that is having all the sides with equal measure i.e. all the sides are of same length. Any shape has rotational symmetry that will still look the same after the rotation.