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=(360)/(n)`

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

`\begin{gathered} a_(20)=(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°)