We know that, usually,
[tex] c^2 = a^2+b^2 [/tex]
In this case, we also know that
[tex] c^2 = 2ab [/tex]
We deduce that
[tex] a^2+b^2 = 2ab [/tex]
If we subtract 2ab from both sides, we get
[tex] a^2-2ab+b^2 = 0 \iff (a-b)^2 = 0 \iff a=b [/tex]
So, the triangle is an isosceles right triangle, and so the angles are 90-45-45
