Question

PLEASE HELP!!!! What is the smallest degree of rotation that will map a regular 20-gon onto itself?

Answer 1

Answer: $18^{\circ}$

Step-by-step explanation:

For a regular 20-gon, since  there are 20 vertices that the polygon can be rotated  and be mapped onto itself .Thus the order of symmetry of 20-gon is 2.

To find the degrees of rotational symmetry, we need to divide 360° by the order of symmetry.

Thus, the degree of rotation=$\frac{360^{\circ}}{20}=18^{\circ}$

Hence,  the smallest degree of rotation that will map a regular 20-gon onto itself=$18^{\circ}$