[tex]\it AB=AC \Rightarrow \Delta ABC-isoscel \Rightarrow \hat B=\hat C\ \ \ \ \ \ (1)\\ \\ \Big[ BD-bisectoare \Rightarrow \widehat{ABD}=\widehat{DBC}\ \stackrel{not}{=}\ x\ \ \ \ \ \ (2)\\ \\ \Delta ABC \sim \Delta BDC \Rightarrow \dfrac{AB}{BD}=\dfrac{AC}{BC}\ \ \ \ \ \ (3)\\ \\ \\ AB=AC\ \ \ \ \ \ \ (4)\\ \\ (3),\ (4) \Rightarrow BD=BC \Rightarrow \Delta DBC-isoscel \Rightarrow \widehat{CDB}=\widehat{BCD}=2x[/tex]
Suma măsurilor unghiurilor triunghiului BCD este:
[tex]\it x+2x+2x=180^o \Rightarrow 5x=180^o|_{:5} \Rightarrow x=36^o \Rightarrow \begin{cases} \it \hat A=36^o\\ \\ \it \hat B=\hat C=72^o\end{cases}[/tex]
