What is the smallest angle of rotational symmetry that maps a regular octagon onto itself? enter your answer in the box.

45 Degrees is the smallest angle of rotational symmetry that maps a regular octagon onto itself

Solution-

A regular octagon has 8 equal angles and 8 equal sides.  

When rotating an octagon around its center, 1/8th of a full-circle rotation will cause adjacent sides to coincide on each other.

A circle has 360° and (1/8)th of 360° = 45°.  

Hence, a minimum of 45° rotation counterclockwise or clockwise(as it is symmetric so the order doesn't matter) puts each of the edges over the position where an adjacent edge was located before.

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

4444444444444 i think