Question

in patrulaterul convex ABCD m<(A)=75grade ,iar masurile unghiurilor B,C,D, sunt invers proportionale cu 0,1(6) , 1supra 4, 0,1(1).
calculati masurile unghiurilor patrulaterului ABCD.
VA ROG FOARTE MULT RASPUNDETI PANA MAINE DIMINEATA MAXIM ORA 10 00

Answer 1

patrulaterul are masura unghiurilor =360 grade
deci masura unghiurilor B,C,D=360-75=285
a=75
b+c+d=285
0,1(6)=(16-1)/90=15/90=5/30
0,1(1)=(11-1)/90=12/90=4/30
{b,c,d}i.p.{5/30,1/4,4/30}
5b/30=c/4=4d/30=k
5b/30=k⇒b=30k/5
c/4=k    ⇒c=4k
4d/30=k⇒d=30k/4
30k/5+4k+30k/4=285
(120k+80k+150k)/20=285
350k=285x20
k=5700/350=570/35=114/7
b=30k/5=[30x114/7)]/5=(30x114)/(7x5)=3420/35=684/7=97,71
b≈98
c=4k=4x114/7=456/7≈65
c=≈65
d=30k/4=(30x114/7)/4=(30x114)(7x4)=3420/28
d=≈≈122
98+65+122=285