One to Two,Isosceles to Isosceles

Geometry Level 3

One possible way to draw \(ABC\) and split it into two isosceles triangles is shown here.

One possible way to draw \(ABC\) and split it into two isosceles triangles is shown here.

An isosceles triangle \(ABC\) \((\)with \(\angle B=\angle C)\) is cut into two smaller isosceles triangles (which don't have to be identical).

How many different possible angles \(\angle A\) are there?

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