How many sides does a regular poly gon have with the measure of the interior angle as 179°?

Interior angles of any polygon with n sides always add up to 180(n-2) degrees. 

If a polygon is a regular polygon with n sides, and each interior angle is 179 degrees, then its interior angles will add up to 179 n. 

In both cases, you must get the same result for what the interior angles add up to. So: 

179n = 180(n-2). Multiply out the 180 

179n = 180n - 360, and subtract 180n from both sides to get 

-n = -360, so therefore n = 360 and it would have 360 sides.