# 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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