jmc

The sum of the interior angles of a polygon is $180(n-2)$, where $n$ is the number of sides. That means each interior angle has a measure of $\frac{180(n-2)}{n}$ degrees. We set this equal to 170 degrees and solve for $n$. $$\begin{array}{rl}\frac{180(n-2)}{n}& =170\\ \Rightarrow 180n-360& =170n\\ \Rightarrow 10n& =360\\ \Rightarrow n& =36.\end{array}$$ The polygon has $\boxed{36}$ sides.