I know that the sum of the interior angles of a polygon with n sides is (n-2) times 180 degrees. So if each angle measures 170 degrees, then the sum is n times 170 degrees. I can set these two expressions equal to each other and solve for n. (n-2) times 180 = n times 170. I can simplify this by dividing both sides by 10. (n-2) times 18 = n times 17. I can expand the brackets and move everything to one side. 18n - 36 = 17n. n = 36. So the polygon has 36 sides. 
Each interior angle of a polygon measures 170 degrees. How many sides does the polygon have?