Question

In a regular polygon with n sides, what is the smallest angle of rotation about the center for which the polygon will be mapped onto itself? A. n B. n/360 C. 360/n D. 180/n

Answer 1

Explanation:

A polygon in the plane has rotational symmetry if the figure can be mapped onto itself by rotating between 0 and 360° about it's center.

So, we need to find the number of symmetrical line a regular polygon can have.

Note : A regular polygon with n sides has n lines of symmetry and order of symmetry n.

Then, let n be number of symmetrical line lines

Then,

Smallest angle of rotation about the center for which the polygon will be mapped unto itself is

360 / n