Question

Va rog daca puteti sa rezolvati

Answer 1

Notăm măsurile unghiurilor cu x,  y,  z.

$\it x+y+z=180^o\ \ \ \ \ (1)\\ \\ \\ \{x,\ \ y,\ \ z\}\ i.\ p.\ \Big\{\dfrac{1}{3},\ \dfrac{1}{2},\ \dfrac{1}{4}\Big\} \Rightarrow \{x,\ \ y,\ \ z\}\ d.\ p.\ \{3,\ \ 2,\ \ 4\} \Rightarrow \\ \\ \\ \Rightarrow \dfrac{x}{3}=\dfrac{y}{2}=\dfrac{z}{4}=\dfrac{x+y+z}{3+2+4}\stackrel{(1)}{=}\ \dfrac{180^o}{9}=20^o\ \ \ \ \ (2)$

$\it (2) \Rightarrow \begin{cases} \it \dfrac{x}{3}=20^o \Rightarrow x=3\cdot20^o=60^o\\ \\ \it \dfrac{y}{2}=20^o \Rightarrow y=2\cdot20^o=40^o\\ \\ \it \dfrac{z}{4}=20^o \Rightarrow z=4\cdot20^o=80^o\end{cases}$