Inscribed triangle

A circle is an inscribed triangle, and its vertices divide the circle into three arcs. The length of the arcs is in the ratio 2:3:7. Find the interior angles of a triangle.

Correct answer:

α =  30 °
β =  45 °
γ =  105 °

Step-by-step explanation:

$$\begin{gathered} a:b:c=2:3:7=\alpha :\beta :\gamma \\ \omega =\frac{180}{2+3+7}=15{}^{\circ } \\ \alpha =2\cdot \omega =2\cdot 15=30^{\circ } \end{gathered}$$

$\beta =3\cdot \omega =3\cdot 15=45^{\circ }$

$\gamma =7\cdot \omega =7\cdot 15=105^{\circ }$

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