Break up the polygon in your head. Maybe draw a picture of the polygon as a bunch of isosceles triangles that intersect at the center of the circle.
If n stands for the number of sides on the polygon, the angle that goes out from the center is 360/n. That means that the other two angles added together are the angle of the polygon. And since they make up the angle of a triangle, they add to 180 degrees.
NOT difficult at all
So 140+360/n=180
360/n=180-140=40
40*n=360
n=360/40=9
nonagon
+20 
