CMIMC 2019 Team Problem 12

Call a convex quadrilateral angle-Pythagorean if the degree measures of its angles are integers w \leq x \leq y \leq z satisfying

w^{2}+x^{2}+y^{2}=z^{2}

Determine the maximum possible value of x+y for an angle-Pythagorean quadrilateral.