[tex]\{A,B,C\} i.p.\{ \frac{1}{5},\frac{1}{6},\frac{1}{7}\}\Rightarrow \frac{\frac{A}{1}}{\frac{1}{5}}=\frac{\frac{B}{1}}{\frac{1}{6}}=\frac{\frac{C}{1}}{\frac{1}{7}}\Rightarrow \frac{A}{5}=\frac{B}{6}=\frac{C}{6}=K\Rightarrow\\
\Rightarrow A=5k,B=6k, C=7k\\
A+B+C=180\\
5k+6k+7k=180\\
18k=180\\
\boxed{k=10}\\
A=5k\Rightarrow \boxed{A=50}\\
B=6k\Rightarrow \boxed{B=60}\\
C=7k \Rightarrow \boxed{C=70}[/tex]
