It's difficult to picture in my mind what you are describing.
Would a good analogy be like a wheel with angled spokes?
If so, you may be able to use your line to to draw the length and angle of your line, then extrude to your desired size , after which you just use the Circular pattern tool to do the rest.
Please understand I'm just a newbie at this myself but, as it happens, I just finished a drawing that resembles a spoked wheel. The only difference is my spokes weren't angles, they went straight out from my center hub.