Question

afati masurile unghiurilor unui patrulater convex abcd stiind ca unghiurile A,B,C AU masurile direct proportionale 4 5 si 6 iar unghiurile C D au au direct proportionale cu 4 si 5

Answer 1

a/4=b/5=c/6=k
a=4k
b=5k
c=6k
c/4=d/5=k'
c=4k'
d=5k'
6k=4k' =>k=4k'/6=2k'/3
a+b+c+d=360
8k'/3+10k'/3+4k'+5k'=360
8k'+10k'+12k'+15k'=360x3
45k'=1080
k'=24 =>k=16
=>a=64
=>b=80
=>c=96
=>d=120