Răspuns:
[tex]\boldsymbol{ \red{O_1 = 60^{\circ}, O_2 = 80^{\circ}, O_3 = 100^{\circ}, O_4 = 120^{\circ}}}[/tex]
Explicație pas cu pas:
Suma măsurilor unghiurilor formate în jurul unui punct este 360°.
[tex]\hat O_1 + \hat O_2 + \hat O_3 + \hat O_4 = 360^{\circ}[/tex]
{O₁, O₂, O₃, O₄} i.p. {20, 15, 12, 10}
[tex]\dfrac{\hat O_1}{\dfrac{1}{20} } = \dfrac{\hat O_2}{\dfrac{1}{15} } = \dfrac{\hat O_3}{\dfrac{1}{12} } = \dfrac{\hat O_4}{\dfrac{1}{10} } = \dfrac{\hat O_1 + \hat O_2 + \hat O_3 + \hat O_4}{\dfrac{^{3)} 1}{20} + \dfrac{^{4)} 1}{15} + \dfrac{^{5)} 1}{12} + \dfrac{^{6)} 1}{10}} = \\[/tex]
[tex]= \dfrac{360}{\dfrac{3 + 4 + 5 + 6}{60}} = \dfrac{360}{\dfrac{18}{60}} = \dfrac{360 \cdot 60}{18} = 1200\\[/tex]
Măsurile unghiurilor sunt:
[tex]\dfrac{\hat O_1}{\dfrac{1}{20} } = 1200 \Rightarrow \hat O_1 = \dfrac{1200}{20} = \bf 60^{\circ}\\[/tex]
[tex]\dfrac{\hat O_2}{\dfrac{1}{15} } = 1200 \Rightarrow \hat O_2 = \dfrac{1200}{15} = \bf 80^{\circ}[/tex]
[tex]\dfrac{\hat O_3}{\dfrac{1}{12} } = 1200 \Rightarrow \hat O_3 = \dfrac{1200}{12} = \bf 100^{\circ}[/tex]
[tex]\dfrac{\hat O_4}{\dfrac{1}{10} } = 1200 \Rightarrow \hat O_4 = \dfrac{1200}{10} = \bf 120^{\circ}[/tex]
