D is a point on side AC with AD=BC. Find angle DBC.

Solve this without trigonometry.

What if the angle was irrational? Then that would never work. Also, I think there are other "cheating" approaches to this problem, but I don't think those are acceptable.

I don't know how to use the AD = CB information to figure out the answer. The only idea I had was that if triangle ABC was copied so AD matched up with CB, then there would be an angle of 100 degrees. However, no regular polygon has angle measures of 100 degrees.

The only other way I could think of to use this is to put a point E on AB such that AD = AD = BC. Then triangle ADE is similar to triangle ACB, and the longer sides of ADE equal the shorter side of ACB.