Geometry problem

Start with an angle 60 & bisect it,then bisect the lower 30 angle,then the upper 15 angle and so on always alternating between the upper and the lower of previous two angles constructed.This process approaches a limiting line that divides the original angle into two angles.The measure of the smaller angle is?

It's a disguised series problem! It looks like our nth term would be 60/2^n

Yes , but the nth term  go to zero when n go to infinity , so the angle is 0 grade , i guess.

Yes, that answer is "valid" (particularly since it's almost meaningless to talk of an angle at 0 degrees, we may as well say it becomes a line), assuming limits are justified, etc. An infinitesimal answer would also be permissible