Question

In patrulaterul convex ABCD, masurile unghiurilor A,B,C,D sunt in in proportionalitate inversa cu nr. 0,(3);0,2;1 supra 7 si 0,(1)
a) Calculaati masurile unghiurilor patrulaterului  

Answer 1

0,(3)=3/9 SIMPLIFICAM CU 3=1/3                  K-O CONSTANTA
0,2=2/10 SIMPLIF.CU 2=1/5
0,(1)=1/9
{A,B,C,D,}IP{1/3,1/5,1/7,1/9}
A/3=B/5=C/7=D/9=K
A/3=K⇒   A=3K
B/5=K⇒   B=5K
C/7=K⇒   C=7K
D/9=K⇒   D=9K
A+B+C+D=360 GRADE INLOCUIM IN RELATIE CU K
3K+5K+7K+9K=360
24K=360
K=360/24
K=15
A=3K=3·15=45 GRADE
B=5K=5·15=75 GRADE
C=7K·=7·15=105 GRADE
D=9K=9·15=135 GRADE
DECI
45+75+105+135=360