Question

Aflati masurile unghiurilor unui patrulater convex stiind ca sunt invers proportionale cu 0, 5 ; 0, (3); 0, 25 si 0, 1 (6)

Answer 1

0,5·w=0,(3)·x=0,25·y=0,1(6)·z
$\frac{5}{10}$·w=$\frac{3}{9}$·x=$\frac{1}{4}$·y=$\frac{15}{90}$·z=k
$\frac{w}{2}$=$\frac{x}{3}$=$\frac{y}{4}$=$\frac{z}{6}$=k
w=2k
x=3k
y=4k
z=6k
w+x+y+z=360
15k=360
k=24
⇒w=48
x=72
y=96
z=144

Sper ca te-am ajutat! D

Answer 2

$Notez~cu~a,b,c~si~d~masurile~unghiurilor~patrulaterului. \\ \\ 0,5= \frac{1}{2} \\ 0,(3)= \frac{1}{3} \\ 0,25= \frac{1}{4} \\ 0,1(6)= \frac{16-1}{90}= \frac{15}{90}= \frac{1}{6} \\ \\ a*0,5=b*0,(3)=c*0,25=d*0,1(6) \Leftrightarrow \\ \\ \Leftrightarrow a* \frac{1}{2}=b* \frac{1}{3}=c* \frac{1}{4}= d*\frac{1}{6} \Leftrightarrow \\ \\ \Leftrightarrow \frac{a}{2}= \frac{b}{3} = \frac{c}{4}= \frac{d}{6} = \frac{a+b+c+d}{2+3+4+6}= \frac{360 \textdegree}{15}= 24 \textdegree.$

$\frac{a}{2}=24 \textdegree \Rightarrow a=48 \textdegree. \\ \frac{b}{3} =24 \textdegree \Rightarrow b=72 \textdegree. \\ \frac{c}{4}=24 \textdegree \Rightarrow c=96 \textdegree. \\ \frac{d}{6}=24 \textdegree \Rightarrow d= 144 \textdegree.$