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

Question

parthkohli · Answer

Hey Fareeda! I'd start out with:

$\Huge \mathtt{\text{Welcome to OpenStudy!}}$

parthkohli · Answer

When an exterior angle is 36 degrees, then the interior angle is 180 - 36 = 144 degrees, right?

parthkohli · Answer

Now the formula for one angle of a regular polygon is:

$ \color{Black}{\Rightarrow \large \Large {180(n - 2) \over n} }$

You equate that with 144 to find n

$ \color{Black}{\Rightarrow \Large {180(n  - 2) \over n} = 144}$

parthkohli · Answer

When you find $n$, multiply $n$ to 144 for getting the sum of the measures.

parthkohli · Answer

Can you do it now, @fareeda ?