Question

Daca masura unui unghi al unui triunghi este egala cu media aritmetica a masurilor celorlalte doua unghiuri , atunci masura acestuia este.....

Answer 1

    
$Notatii: \\ \alpha = primul ~unghi \\ \beta = al~doilea~unghi \\ \gamma = al~treilea~unghi \\ \\ Rezolvare: \\ \\ \alpha+ \beta +\gamma=180^o~~~~~~~dar~~~ \alpha = \frac{\beta +\gamma}{2} \\ \\ \frac{\beta +\gamma}{2} + \beta +\gamma=180^o~~~~~ Aducem ~la ~acelasi~ numitor. \\ \\ \frac{\beta +\gamma}{2} + \frac{2\beta }{2} + \frac{2\gamma}{2} = \frac{2\;\cdot\;180}{2} ~~~~~~~ |* 2 \\ \\ \beta +\gamma +2\beta +2\gamma = 360$


$(\beta +\gamma) +2(\beta +\gamma) = 360 \\ 3(\beta +\gamma)=360 \\ \beta +\gamma = \frac{360}{3} = 120^o \\ \\ \alpha = \frac{\beta +\gamma}{2} =\frac{120}{2}=\boxed{60^o}$