Question

10.Aflati masurile unghiurilor unui patrulater convex , stiind ca sunt direct proportionale cu numerele 11 , 15 , 21 si 25 11.Aflati masurile unghilor unui patrulater convex ABCD stiind ca unghiurile A,B,C au masurile direct proportionale cu 4, 5 si 6 iar unghiurileC si D au masurile direct proportionale cu 14 si 5.

Answer 1

10)
a/11=b/15=c/21=d/25
b=15a/11
c=21a/11
d=25a/11
a+b+c+d=360°
a+15a/11+21a/11+25a/11=360°
11a+15a+21a+25a=3960°
72a=3960°
a=55°
b=15a/11=15×55°/11=75°
c=21a/11=21×55°/11=105°
d=25a/11=25×55°/11=125°


11)
a/4=b/5=c/6=k
a=4k
b=5k
c=6k

c/14=d/5=m
c=14m
6k=14m      m=6k/14=3k/7      d=5m=5×3k/7=15k/7
a+b+c+d=360°
4k+5k+6k+15k/7=360°
28k+35k+42k+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°