Question

Fie un patrulater convex ABCD, cu măsura unghiurilor direct proporționale cu 3, 4,5,6. aflați măsura unghiurilor patrulaterului convex

Answer 1

a+b+c+d=360°
a/3=b/4=c/5=d/6
b=4a/3
c=5a/3
d=6a/3=2a
a+4a/3+5a/3+2a=360°
a+9a/3+2a=360°
3a+9a+6a=1080°
18a=1080°
a=60°
b=4×60°/3=80°
c=5×60°/3=100°
d=2a=2×60°=120°

Answer 2

a+b+c+d=360° (suma unghiurilor intr-un patrulater convex=360°)
a,b,c,d, d.p. cu {3,4,5,6}  deci ⇒

 a/3=b/4=c/5=d/6=(a+b+c+d)/3+4+5+6

a/3=360/18

a=(360×3):18=60°

b=(360×4):18=80°

c=(360×5):18=100°

d=(360×6):18=120°