Let's make a triangle with the solution

Algebra Level 5

Let T1T_1 be a triangle with angles 57,60,6357^{\circ}, 60^{\circ}, 63^{\circ} and sides a,b,ca, b,c. Let x,y,zx,y,z be positive numbers such that: x(y+zx)=a2,y(z+xy)=b2,z(x+yz)=c2.\begin{aligned} x(y+z-x)=a^2, \\ y(z+x-y)=b^2, \\ z(x+y-z)=c^2. \end{aligned} It is known that x,y,zx,y,z represent the sides of a triangle T2T_2. Find the measure (in degrees) of the greatest angle of T2T_2.

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