Question

Masurile unghiurilor unui patrulater convex sunt invers proportionale su numerele 1 supra 2, 1 supra 3, 1 supra 6 si 1 supra 7. Calculati masurile unghiurilor considera
As vrea sa fie rezolvat cu ipoteza, conclusie, demonstratie

Answer 1

a+b+c+d=360
{a,b,c,d}i.p.{1/2,1/3,1/6,1/7}
a/2=b/3=c/6=d/7=k
a/2=k⇒a=2k
b/3=k⇒b=3k
c/6=k⇒c=6k
d/7=k⇒d=7k
2k+3k+6k+7k=360
18k=360
k=360/18
k=20
a=2k=2··20=40 deci unghiul A are 40 grade
b=3k=3··20=60   unghiul B=60grade
c=6k=6··20=120
d=7k=7·20=140

40+60+120+140=360