[tex]\it Fie\ x,\ y,\ z,\ t\ m\breve asurile\ celor\ patru\ unghiuri.\\ \\ \{x,\ y,\ z,\ t\}\ d.\ p.\ \{3,\ 6,\ 2,\ 4\} \Rightarrow \dfrac{x}{3}=\dfrac{y}{6}=\dfrac{z}{2}=\dfrac{t}{4}=k \Rightarrow \\ \\ \\ \Rightarrow \begin{cases} \it x=3k\\ \\ \it y=6k\\ \\ \it z=2k\\ \\ \it t=4k\end{cases}\ \ \ \ \ \ (*)\\ \\ \\ x+y+z+t=360^o\ \stackrel{(*)}{\Longrightarrow}\ 3k+6k+2k+4k=360^o \Rightarrow 15k=360^o \Rightarrow\\ \\ \\ \Rightarrow k=360^o:15 \Rightarrow k=24^o[/tex]
[tex]\it k=24^o \stackrel{(*)}{\Longrightarrow}\ \begin{cases} \it x=3\cdot24^o=72^o\\ \\ \it y=6\cdot24^o=144^o\\ \\ \it z=2\cdot24^o=48^o\\ \\ \it t=4\cdot24^o=96^o\end{cases}[/tex]
