Question

Is it possible to have a regular polygon whose each interior angle is :
${170}^o$

Answer 1

If the interior angle is ${170}^o$ the exterior angle is ${10}^o$. The exterior angle of a regular polygon with $n$ sides has a measure of $\frac{360}{n}$ degree. So Since the exterior angle of this polygon has measure ${10}^o$ then it has $\frac{360}{10}=36$ sides