Question

What is the sum of the exterior angles, one at each vertex, of a polygon with 20 sides?A.20B.360C.180D. We need more information

Answer 1

The measure of an exterior angle in a polygon with n sides is given by:

$a_n=\frac{360}{n}$

So, for n = 20, we have the measure of the exterior angles of the polygon with 20 sides:

$\begin{gathered} a_{20}=\frac{360}{20} \\ a_{20}=18\degree \end{gathered}$

Now, to find the sum of all exterior angles, let's multiply the exterior angles by the number of sides of the polygon:

$\begin{gathered} S_{20}=a_{20}\cdot n \\ S_{20}=18\cdot20 \\ S_{20}=360\degree \end{gathered}$

Therefore the sum is equal to 360°, correct option: B.

(The sum of exterior angles of a polygon with n sides is always equal to 360°)