Question

Aclati masurile unghiurilor unui patrulater convex,stiind ca acestea sunt direct proportionale cu numerele 2,4,5 respectiv 7

Answer 1

{A,B,C,D} d.p {2,4,5,7}

A B C D
_=_=_=_=k
2 4 5 7

A
_=2k=2•20=40
2
B
_=4k=4•20=80
4
C
_=5k=5•20=100
5
D
_=7k=7•20=140
7

2k+4k+5k+7k=360
18k=360
k=360÷18
k=20

Answer 2

 fie a,b, c, d unghiurile cautate. 
a,b,c,d dp 2,4,5,7⇒ a/2=b/4=c/5=d/7=k
⇒ a=2k,b=4k,c=5k,d=7k.

a+b+c+d=360° (suma unghiurilor intr-un patrulater convex=360°)
2k+4k+5k+7k=360
18k=360
k=360:18
k=20

⇒ a=2k,b=4k,c=5k,d=7k.

a=2k=40°

b=4k=80°

c=5k=100°

d=7k=140°