[tex]\it Fie\ x,\ y,\ z\ m\breve asurile\ celor\ trei\ unghiuri.\\ \\ x+y+z=180^o\ \ \ \ \ (1)\\ \\ \{x,\ y,\ z\}\ i.\ p.\ \{6,\ 4,\ 3\} \Rightarrow 6x=4y=3z=k \Rightarrow \begin{cases}\it x=\dfrac{k}{6}\\ \\ \it y=\dfrac{k}{4}\\ \\ \it x=\dfrac{k}{3}\end{cases}\ \ \ \ (2)[/tex]
[tex]\it \dfrac{k}{6}+\dfrac{k}{4}+\dfrac{k}{3}=180^o|_{\cdot12} \Rightarrow 2k+3k+4k=12\cdot180^o \Rightarrow 9k=12\cdot180^o|_{:9}\Rightarrow\\ \\ \\ \Rightarrow k=12\cdot20^o \Rightarrow k=240^o\ \ \ \ \ (3)\\ \\ \\ (2),\ (3) \Rightarrow \begin{cases} \it x=\dfrac{240^o}{6}=40^o\\ \\ \it y=\dfrac{240^o}{4}=60^o\\ \\ \it z=\dfrac{240^o}{3}=80^o\end{cases}[/tex]
