The circle is divided in the ratio 7:11:6, and the division points are connected to each other. Find the angles of the resulting triangle.

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An inscribed angle is measured by half the angular magnitude of the corresponding arc.

## Solution

One part of the circle corresponds to $\frac{360^{\circ}}{7+11+6}=15^{\circ}$. Therefore, the angular magnitudes of the obtained arcs are

![](https://cdn.mathpix.com/cropped/2024_05_06_845c09db4774ba28be39g-24.jpg?height=63&width=1452&top_left_y=460&top_left_x=17)

![](https://cdn.mathpix.com/cropped/2024_05_06_845c09db4774ba28be39g-24.jpg?height=369&width=378&top_left_y=519&top_left_x=840)

## Answer

$52.5^{\circ} ; 82.5^{\circ} ; 45^{\circ}$.