How do you find out the top angle of an Isosceles triangle if you do not know the base angle?

It depends on whether you know the lengths of all three sides (either explicitly or otherwise). If you don't know the lengths of the sides you cannot find the top angle.

If you do know the sides you can apply the cosine rule:

cos(A) = (b2 +c2 - a2)/2bc and then use the inverse cosine function to determine A.