Question

A regular figure has rational symmetry about its center so that every time it is rotated 10 degrees it looks exactly the same. What is the minimum number of sides this figure must have? Justify your reasoning.

Answer 1

Problem

A regular figure has rational symmetry about its center so that every time it is rotated 10 degrees it looks exactly the same. What is the minimum number of sides this figure must have? Justify your reasoning.​

Solution

For this case we can do the following operation

360/ 10= 36

and we can conclude that we need to have a hexatriacontagon.

And the reason is because we need to satisfy that the sum of the rotation in a circle needs to be equal to the n times sides of the polygon