Let's make a triangle with the solution

Algebra Level 5

Let \(T_1\) be a triangle with angles \(57^{\circ}, 60^{\circ}, 63^{\circ}\) and sides \(a, b,c\). Let \(x,y,z\) be positive numbers such that: \[\begin{align} x(y+z-x)=a^2, \\ y(z+x-y)=b^2, \\ z(x+y-z)=c^2. \end{align} \] It is known that \(x,y,z\) represent the sides of a triangle \(T_2\). Find the measure (in degrees) of the greatest angle of \(T_2\).

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