angular dimension exterior angle of hexagon

I've a simple hexagon, drawn using the polygon toolbar option.  I am trying to dimension the angles and have not been able to figure out how to dimension the outside angle (240 degrees).   Each time I use the angle dimension tool it creates either a 60 degree angle.  By drawing extension lines I was able to get a 120 degree angle.  I tried using the oblique option but it didn't change the situation.  I've tried with and without esnaps enabled. 

I must be overlooking something pretty simple. How do I create the dimension for the exterior angle of a polygon?

Thanks!