Answer: [tex]18^{\circ}[/tex]
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=[tex]\frac{360^{\circ}}{20}=18^{\circ}[/tex]
Hence, the smallest degree of rotation that will map a regular 20-gon onto itself=[tex]18^{\circ}[/tex]
