How is this angle measured in the triangle?

Given the image below:

Let the angle at vertex A be called $\alpha $. Polya says by looking at the diagram and the isoceles triangles $\mathrm{\u25b3}ACE$ and $\mathrm{\u25b3}ABD$ we can deduce that $\mathrm{\angle}DAE=\frac{\alpha}{2}+90\xb0$.

Where will I get $90\xb0$ from?

Given the image below:

Let the angle at vertex A be called $\alpha $. Polya says by looking at the diagram and the isoceles triangles $\mathrm{\u25b3}ACE$ and $\mathrm{\u25b3}ABD$ we can deduce that $\mathrm{\angle}DAE=\frac{\alpha}{2}+90\xb0$.

Where will I get $90\xb0$ from?