Find how many sides a polygon has

There is a formula that relates the number of sides of a regular polygon to its interior angle. It is the following:

 

\(\frac{180(n-2)}{n}\)

 

This formula will tell you the interior angle measure, if given the number of sides. However, we have the interior angle measure! So, just solve for n, the number of sides.

 

\(\frac{180(n-2)}{n}=170\)	Multiply by n on both sides to get rid of the pesky fraction.
\(180(n-2)=170n\)	We can divide both sides by 10 to keep the numbers relatively small.
\(18(n-2)=17n\)	Distribute inside of the paretheses.
\(18n-36=17n\)	Subtract 18n from both sides.
\(-36=-n\)	Divide by -1 on both sides to isolate n.
\(n=36\)

 

Therefore, this polygon has 36 sides.