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

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=

Hence,  the smallest degree of rotation that will map a regular 20-gon onto itself=

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°