Question

Aflati masura unghiului unui triunghi , stiind ca ele sunt proportionale cu numerele 2, 3 ,5

Answer 1

<A=<B=<C
A+B+C=180 (suma unghiurilor unui triunghi este 180 grade)
{A,B,C} d.p. (2,3,5}
A/2=B/3=C/5=K (K este constanta)
A/2=K ⇒A=2K
B/3=K⇒B=3K
C/5=K⇒C=5K
A+B+C=2K+3K+5K
⇒2K+3K+5K=180
    10K=180
    K=180/10
    K=18⇒A=2K=2*18=36
                B=3K=3*18=54
                C=5K=5*18=90

Verificare :
A+B+C=180
36+54+90=180
90+90=180
180=180

Answer 2

$Un~triunghi~are~3~unghiuri ~ ! Notam~masurile~unghiurilor~cu~x~,~y~,~z Suma~celor~3~unghiuri~in~triunghi~este~de~180~de~grade = \ \textgreater \ Suma~180 x + y + z = 180 \left \{ {{x} \atop {y}} \atop {z}\right. d.p. \left \{ {{2} \atop {3}} \atop {5}\right. \frac{x}{2} = \frac{y}{3} = \frac{z}{5} = K = \ \textgreater \ \frac{x}{2} = K = \ \textgreater \ x = 2 * K = \ \textgreater \ \boxed {x = 2K } \frac{y}{3} = K = \ \textgreater \ y = 3 * K = \ \textgreater \ \boxed{ y = 3K } \frac{z}{5} = K = \ \textgreater \ z = 5 * K = \ \textgreater \ \boxed{z = 5K } x + y + z = 180 = \ \textgreater$$2K + 3K + 5K = 180 = \ \textgreater \ 5K + 5K = 180 = \ \textgreater \ 10K = 180 = \ \textgreater \ K = \frac{180}{10} = \ \textgreater \ \boxed{K = 18~ ( constanta~de~proportionalitate} x = 2K = 2 * 18 = \underline{ 36 } y = 3K = 3 * 18 = \underline{54} z = 5K = 5 * 18 = \underline{90} Masurile~unghiurilor~sunt~\underline{15~,~36~,~39~.}$