Question

aflati masurileunghiurilor unui patrulater convex abcd stiindca unghiurile a bc sunt direct proportionale cu 4 5 6 iar unghiurile c si d au masurile direct proportionale cu 14 si 5

Answer 1

a/4=b/5=c/6=k      c=6k
c/14=d/5=m          c=14m      6k=14m  m= 6k/14=3k/7    d=5m=5×3k/7=15k/7
a=4k
b=5k
c=6k
d=15k/7
a+b+c+d=360°
4k+5k+6k+15k/7=360°
15k+15k/7=360°
105k+15k=2520°
120k=2520°
k=21°
a=4k=4×21°=84°
b=5k=5×21°=105°
c=6k=6×21°=126°
d=15k/7=15×21°/7=45°

Answer 2

a/4=b/5=c/6=k      c=6k
c/14=d/5=m          c=14m      6k=14m  m= 6k/14=3k/7    d=5m=5×3k/7=15k/7
a=4k
b=5k
c=6k
d=15k/7
a+b+c+d=360°
4k+5k+6k+15k/7=360°
15k+15k/7=360°
105k+15k=2520°
120k=2520°
k=21°
a=4k=4×21°=84°
b=5k=5×21°=105°
c=6k=6×21°=126°
d=15k/7=15×21°/7=45°