you can only approximate the angles of the real thing, but certain approximations will look cleaner than others. In general, you want your diagonal lines to have a consistent number of pixels in their staggered segments.
A 45 degree line 
goes one pixel to the side for each pixel it goes vertically. A approx. 27 degree line 
goes two pixels to the side for each pixel it goes vertically. [This angle can be found by taking the inverse tangent of 1/2.] We can do a decent approximation of a lot of simple regular polygons using various combinations of the these angles!
Triangle
Two 27 degree angles add up to close enough to 60. 
Square
I'll let you figure this one out on your own.
Hexagon
90 + 27 is a great approximation of 120 