Question

Patrulaterul ABCD are masurile unghiurilor A B C si D i.p cu numerele 0,(3) ; 0,25 ; 0,2 si 0,1(6) . Aflati masura unghiurilor A B C si D in grade

Answer 1

$\it 0,(3)=\dfrac{\ 3^{(3}}{9}=\dfrac{1}{3}\\ \\ \\ 0,25=\dfrac{\ 25^{(25}}{100}=\dfrac{1}{4}\\ \\ \\ 0,2=\dfrac{\ 2^{(2}}{10}=\dfrac{1}{5} \\ \\ \\ 0,1(6)=\dfrac{16-1}{90}=\dfrac{\ 15^{(15}}{90} = \dfrac{1}{6}\\ \\ \\ \{A,\ B,\ C,\ D\}\ i.\ p.\ \Big\{\dfrac{1}{3},\ \dfrac{1}{4},\ \dfrac{1}{5},\ \dfrac{1}{6}\Big\}\Rightarrow \{A,\ B,\ C,\ D\}\ d.\ p.\{3,\ 4,\ 5,\ 6\} \Rightarrow$

$\it \Rightarrow \dfrac{A}{3}=\dfrac{B}{4}=\dfrac{C}{5}=\dfrac{D}{6} =\dfrac{A+B+C+D}{3+4+5+6}=\dfrac{360^o}{18}=20^o\\ \\ \\ \dfrac{A}{3}=20^o \Rightarrow A=3\cdot20^o =60^o \\ \\ \\ \dfrac{B}{4}=20^o \Rightarrow B=4\cdot20^o =80^o \\ \\ \\ \dfrac{C}{5}=20^o \Rightarrow C=5\cdot20^o =100^o$