Question

Aflați măsurile unghiurilor unui patrulater convex, ştiind că:
a)Sunt direct proporționale cu numerele: 2,5 ,2 ,1,5 şi 3.
b)Invers proporționale cu numere: 2/3, 1, 2, 3.

Answer 1

a) a+b+c+d=360°
2,5=25/10=5/2
1,5=15/10=3/2
2a/5=b/2=2c/3=d/3=k
a=5k/2
b=2k
c=3k/2
d=3k
5k/2 + 2k + 3k/2 + 3k = 360
5k+4k+3k+6k=720
18k=720 => k=40
a=(5•40)/2=100
b=80
c=(3•40)/2=60
d=120

b) a+b+c+d=360°
2a/3=b=2c=3d=k
a=3k/2
b=k
c=k/2
d=k/3
3k/2 + k + k/2 + k/3 = 360
9k+6k+3k+2k=2160
20k=2160 => k=108
a=(3•108)/2=162
b=108
c=108/2=54
d=108/3=36