a)
[tex]\bf C(O;r)=360^{\circ}\Rightarrow\overset{\frown}{AB}+\overset{\frown}{BC}+\overset{\frown}{CA}=360^{\circ}[/tex]
[tex]\bf O \subset \measuredangle AOB \Rightarrow \measuredangle AOB - \measuredangle \: la \; centru[/tex]
[tex]\bf \Rightarrow \overset{\frown}{AB}=\measuredangle AOB=60^{\circ}[/tex]
[tex]\bf x\% \; din \; 360^{\circ}=60^{\circ}[/tex]
[tex]\bf \Rightarrow \dfrac{x}{100} \cdot 360^{\circ}=60^{\circ}\Rightarrow \dfrac{x}{10} \cdot 36 =60\;\;\bigg|\cdot 10[/tex]
[tex]\bf \Rightarrow 36x=600\; \;\bigg|:36 \Rightarrow \red{\boxed{\bf x=16,(6)\%}}[/tex]
b)
[tex]\bf O \subset \measuredangle BOC \Rightarrow \measuredangle BOC - \measuredangle \: la \; centru[/tex]
[tex]\bf \Rightarrow \overset{\frown}{BC}=\measuredangle BOC = 90^{\circ}[/tex]
[tex]\bf x\% \; din \; 360^{\circ}=90^{\circ}[/tex]
[tex]\bf \Rightarrow \dfrac{x}{100} \cdot 360 = 90 \Rightarrow \dfrac{x}{10} \cdot 36=90 \; \;\bigg|\cdot 10[/tex]
[tex]\bf \Rightarrow 36x=900\;\;\bigg| :36 \Rightarrow \purple{\boxed{\bf x=25\%}}[/tex]
c)
[tex]\bf \measuredangle COD \leq 180^{\circ}[/tex]
[tex]\bf 50\% \: din \; 360^{\circ}=\measuredangle COD = x[/tex]
[tex]\bf \Rightarrow \dfrac{50}{100}^{(50} \cdot 360=x \Rightarrow \dfrac{1}{2} \cdot 360=x[/tex]
[tex]\bf \Rightarrow x=\dfrac{360^{\circ}}{2} \Rightarrow \pink{\boxed{\bf x=180^{\circ}}}[/tex]
