Question

determinati masurile unui patrulater convex stiind ca masurile unghiurilor sunt direct proportionale cu 2,3,7 si8

Answer 1

ABCD - patrulater
A=2x
B= 3x
C =7x
D=8x 
2x+3x+7x+8x = 360
20x=360
x= 360/20
x= 18
A=2*18=36
B=3*18=54
C=7*18=126
D=8*18=144

Answer 2

notam cu a,b,c si d cele 4∡ale patrulaterului⇒a+b+c+d=360°
a/2=b/3=c/7=d/8=k⇒
⇒a/2=k⇒a=2k;b/3=k⇒b=3k;c/7=k⇒c=7k;d/8=k⇒d=8k
a+b+c+d=2k+3k+7k+8k=360°⇒20k=360°⇒k=18°
a=2k=2×18°⇒a=36°;b=3k=3×18°⇒b=54°;c=7k=7×18°⇒c=126°
d=8k=8×18°⇒d=144°
proba:36°+54°+126°+144°=360°