Inscribed triangle

To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.

Result

α =  30 °
β =  45 °
γ =  105 °

Solution:

a = \dfrac{ 180 ^\circ }{ 2 + 3 + 7} = 15 ^\circ =15^\circ \ \\ \alpha = 2 a = 30 \text{ ^\circ } = 30^\circ
\beta = 3 a = 45 \text{ ^\circ } = 45^\circ
\gamma = 7 a = 105 \text{ ^\circ } = 105^\circ



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