[tex]\it a)\\ \\ \hat B=\hat A\ \ \ \ \ \ (1)\\ \\ \hat C=2\hat A\ \ \ \ (2)\\ \\ \hat A+\hat B+\hat C=180^o\ \stackrel{(1),(2)}{\Longrightarrow}\ \hat A+\hat A+2\hat A=180^o \Rightarrow \\ \\ \Rightarrow4\hat A=180^o|_{:4} \Rightarrow \hat A=45^o\ \ \ \ \ (3)[/tex]
[tex]\it (1),\ (3) \Rightarrow \hat B=45^o\\ \\ (2),\ (3) \Rightarrow \hat C=2\cdot45^o=90^o[/tex]
[tex]\it b)\\ \\ \hat A=2\hat B\ \ \ \ \ \ (1)\\ \\ \hat C=3\hat B+12^o\ \ \ \ (2)\\ \\ \hat A+\hat B+\hat C=180^o\ \stackrel{(1),(2)}{\Longrightarrow}\ 2\hat B+\hat B+3\hat B+12^o=180^o|_{-12^o} \Rightarrow \\ \\ \Rightarrow 6\hat B=168^o|_{:6} \Rightarrow \hat B=28^o\ \ \ \ \ (3)[/tex]
[tex]\it (1),\ (3) \Rightarrow \hat A=2\cdot28^o=56^o\\ \\ (2),\ (3) \Rightarrow \hat C=3\cdot28^o+12^o =96^o[/tex]
[tex]\it c)\\ \\ \hat A=3\hat C\ \ \ \ \ \ (1)\\ \\ \hat B=\hat A+12^o=3\hat C+12^o\ \ \ \ (2)\\ \\ \hat A+\hat B+\hat C=180^o\ \stackrel{(1),(2)}{\Longrightarrow}\ 3\hat C+3\hat C+12^o+\hat C=180^o|_{-12^o} \Rightarrow \\ \\ \Rightarrow 7\hat C=168^o|_{:7} \Rightarrow \hat C=24^o\ \ \ \ \ (3)[/tex]
[tex]\it (1),\ (3) \Rightarrow \hat A=3\cdot24^o=72^o\\ \\ (2),\ (3) \Rightarrow \hat B=3\cdot24^o+12^o =84^o[/tex]
