Question

What are the angles of rotation for a 20-gon?

Answer 1

Hint: To find the angle of rotation for this polygon, we will draw a small circle inside the polygon. We will divide the central angle of a circle by the number of sides of the polygon to get the angle of rotation for the polygon.
A rotation is a transformation that turns every point of a given figure through a specified angle, in a particular direction. Angles are usually measured in degrees, radians, gons, and turns.

Complete step by step solution:
We have a regular polygon with 20 sides. This means that the central angle is divided into 20 equal parts. Constructing a small circle inside the polygon, we have the required figure.

Now, since the central angle of the circle is ${360}^{\circ }$ , it is equally divided into 20 equal parts. So, the angle of rotation will be given by
$\begin{array}{rl}& {\displaystyle \frac{{360}^{\circ }}{20}}\\ & ={18}^{\circ }\end{array}$
This means that the angle subtended by each side of a 20-sided regular polygon at the center is ${18}^{\circ }$.

Note: Kindly note that there is a difference between angle of rotation and interior angle of a polygon. While the interior angle of a polygon is the angle contained between two sides of a polygon, angle of rotation is the angle subtended by a side at the center of the polygon.
For a n-sided polygon
Sum of interior angles$={180}^{\circ }(n-2)$
Angle of rotation$={\displaystyle \frac{{360}^{\circ }}{n}}$