To find the number of sides of a regular polygon based on its smallest angle of rotation, we can use the formula for the angle of rotation. The angle of rotation for a regular polygon with n sides is given by:
Angle of rotation = 360° / n
Given that the smallest angle of rotation is 18 degrees, we can set up the equation:
360° / n = 18°
Now, we can solve for n:
Multiply both sides by n:
360° = 18° * n
Now, divide both sides by 18°:
n = 360° / 18°
Calculating this gives us:
n = 20
Therefore, the polygon has 20 sides, which is known as a icosagon.