Is there an addon to improve the knife tool? I see how to use the knife tool to draw shapes by clicking points along, say, an imported image in the background. But I want to know if there is a way to draw 2d shapes with precise angles (90 degree, 30 degree, etc), curves, and precise line lengths, to make closed shapes that one could then extrude into 3d. 

There doesn't appear to be a way to do this with the knife tool (unless I'm missing knife settings somewhere), so perhaps there's an addon that'll do this.

Thanks!
You can try PolyQuilt. It does many other things, but also what you want.
If I remember correctly, once you click the 4th point it closed the quad automaticall, so it may be a bit anoying for you if there is no option to change that or you can't work around it.
In any case, give it a try.