What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 36°?

Question

cwrw238 · Answer

the sum of all exterior angles = 360
so you have a decagon here
sum of interior angles = 10 * (180-36)

cwrw238 · Answer

10 * 144

anonymous · Answer

Well, you know the sum of the interior angles for a polygon with $n$ sides is $(n-2)180^\circ$, so if we divide that into $n$ equal angles (the number of interior angles in such a regular polygon\), we get the following expression for the magnitude of each angle:$$\frac{n-2}{n}180^\circ$$Set that equal to $36^\circ$ and solve for $n$.

sarahc · Answer

okay, thank you! I got that answer too :)

cwrw238 · Answer

yw