Avem A+B+C+D=360°
(A,B,C,D) invers proportional cu (2;3;4;6)
A=[tex] \frac{k}{2} [/tex]
B=[tex] \frac{k}{3} [/tex]
C=[tex] \frac{k}{4} [/tex]
D=[tex] \frac{k}{6} [/tex]
A+B+C+D 360°=>[tex] \frac{k}{2}+ \frac{k}{3} + \frac{k}{4} + \frac{k}{6}=360 [/tex]
si aducem la acelasi numitor, acela fiind 12:
Obtinem : [tex] \frac{6k}{12} + \frac{4k}{12} + \frac{3k}{12}+ \frac{2k}{12}=360°=\ \textgreater \ \frac{15k}{12}=360 [/tex] =>[tex]k= \frac{360*4}{5}= 288[/tex]
Pentru A=>[tex] \frac{288}{2} =144[/tex] °
B=>[tex] \frac{288}{3}=96 [/tex]°
C=>[tex] \frac{288}{4}=72 [/tex]°
D=>[tex] \frac{288}{6}=48 [/tex]°
Deci, masura lui C este 72°
