We have an acute triangle $ABC$. Consider the square $A_1A_2A_3A_4$ which has one vertex in $AB$, one vertex in $AC$ and two vertices ($A_1$ and $A_2$) in $BC$ and let $x_A=\angle A_1AA_2$. Analogously we define $x_B$ and $x_C$. Prove that $x_A+x_B+x_C=90$
