geometry – How is this angle measured in the traingle?

I read "How to solve it" by George Polya. I do not understand how he gets to certain solutions. Like the chapetr of "Auxillary Solution". Given the picture below:

Leave the angle at the top $$A$$ to be called $$alpha$$. Polya says looking at the diagram and the isosceles triangles $$triangle {ACE}$$ and $$triangle {ABD}$$ we can maintain that $$angle {DAE} = frac { alpha} {2} + 90 ^ circ$$.

I just do not understand how this is possible. All I can understand is that $$angle {CAE} = angle {CEA}$$ and $$angle {BAD} = angle {BDA}$$since they are both isosceles. But where will I get $$90 ^ circ$$ of?

Do I miss an important theorem in geometry?