[tex]\it Not\breve am\ cu\ x,\ y,\ z\ m\breve asurile\ celor\ trei\ unghiuri.\\ \\ x+y+z=180^o\ \ \ \ (*)[/tex]
[tex]\bf a)\ \it \{x,y,z\}\ d.p. \{7,\ 11,\ 12\}\ \Rightarrow \dfrac{x}{7}=\dfrac{y}{11}=\dfrac{z}{12}=\dfrac{x+y+z}{7+11+12}\ \stackrel{(*)}{=}\ \dfrac{180^o}{30}=6^o\\ \\ \\ \dfrac{x}{7}=6^o\Rightarrow x=7\cdot6^o \Rightarrow x=42^o\\ \\ \\ \dfrac{y}{11}=6^o\Rightarrow y=11\cdot6^o \Rightarrow y=66^o\\ \\ \\ \dfrac{z}{12}=6^o\Rightarrow z=12\cdot6^o \Rightarrow z=72^o[/tex]
[tex]\bf b)\ \it 0,2=\dfrac{\ 2^{(2}}{10}=\dfrac{1}{5};\ \ 0,(3)=\dfrac{\ 3^{(3}}{9}=\dfrac{1}{3}\\ \\ \\ \{x,\ y,\ z\}\ i.\ p.\ \{\dfrac{1}{5},\ \dfrac{1}{3},\ 1\}\ \Rightarrow \{x,\ y,\ z\}\ d.\ p.\ \{5,\ 3,\ 1\}\ \Rightarrow \dfrac{x}{5}=\dfrac{y}{3}=\dfrac{z}{1}=\\ \\ \\ =\dfrac{x+y+z}{5+3+1}\ \stackrel{(*)}{=}\ \dfrac{180^o}{9}=20^o[/tex]
[tex]\it \dfrac{x}{5}=20^o\Rightarrow x=5\cdot20^o \Rightarrow x=100^o\\ \\ \\ \dfrac{y}{3}=20^o\Rightarrow y=3\cdot20^o \Rightarrow y=60^o\\ \\ \\ \dfrac{z}{1}=20^o\ \Rightarrow z=20^o[/tex]
