Explicație pas cu pas:
▪︎efectuăm transformările:
[tex]0,(3) = \dfrac{3}{9} = \dfrac{1}{3}[/tex]
[tex]0,2 = \dfrac{2}{10} = \dfrac{1}{5}[/tex]
[tex]0,1(6) = \dfrac{16-1}{90} = \dfrac{15}{90} = \dfrac{1}{6}[/tex]
[tex]0,25 = \dfrac{25}{100} = \dfrac{1}{4}[/tex]
▪︎se consideră punctele A,B,C,D (în această ordine) => unghiurile indicate aparțin patrulaterului convex ABCD
▪︎suma unghiurilor unui patrulater convex este 360°
[tex]\dfrac{\hat{A}}{3} = \dfrac{\hat{B}}{5} = \dfrac{\hat{C}}{6} = \dfrac{\hat{D}}{4} = \dfrac{\hat{A} + \hat{B} + \hat{C} + \hat{D}}{3+5+6+4} = \dfrac{360}{18} = 20[/tex]
[tex]\dfrac{\hat{A}}{3} = 20 \implies \hat{B} = {60}^{0} [/tex]
[tex]\dfrac{\hat{B}}{5} = 20 \implies \hat{B} = {100}^{0} [/tex]
[tex]\dfrac{\hat{C}}{6} = 20 \implies \hat{C} = {120}^{0} [/tex]
[tex]\dfrac{\hat{D}}{4} = 20 \implies \hat{D} = {80}^{0} [/tex]
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Explicație pas cu pas:
▪︎efectuăm transformările:
[tex]0,(3) = \dfrac{3}{9} = \dfrac{1}{3}[/tex]
[tex]0,2 = \dfrac{2}{10} = \dfrac{1}{5}[/tex]
[tex]0,1(6) = \dfrac{16-1}{90} = \dfrac{15}{90} = \dfrac{1}{6}[/tex]
[tex]0,25 = \dfrac{25}{100} = \dfrac{1}{4}[/tex]
▪︎se consideră punctele A,B,C,D (în această ordine) => unghiurile indicate aparțin patrulaterului convex ABCD
▪︎suma unghiurilor unui patrulater convex este 360°
[tex]\dfrac{\hat{A}}{3} = \dfrac{\hat{B}}{5} = \dfrac{\hat{C}}{6} = \dfrac{\hat{D}}{4} = \dfrac{\hat{A} + \hat{B} + \hat{C} + \hat{D}}{3+5+6+4} = \dfrac{360}{18} = 20[/tex]
[tex]\dfrac{\hat{A}}{3} = 20 \implies \hat{B} = {60}^{0} [/tex]
[tex]\dfrac{\hat{B}}{5} = 20 \implies \hat{B} = {100}^{0} [/tex]
[tex]\dfrac{\hat{C}}{6} = 20 \implies \hat{C} = {120}^{0} [/tex]
[tex]\dfrac{\hat{D}}{4} = 20 \implies \hat{D} = {80}^{0} [/tex]