$\begin{aligned} & \text { [ Inscribed angle is half of the central angle ] } \\ & \text { [Central angle. Arc length and circumference ]}\end{aligned}$

A chord divides the circle in the ratio 7:11. Find the inscribed angles subtended by this chord.
The angular measure of a full circle is $360^{\circ}$. An inscribed angle is measured by half the angular measure of the corresponding arc.

## Solution

The angular measure of a full circle is $360^{\circ}$. One part is $\frac{360^{\circ}}{7+11}=20^{\circ}$. Therefore, the angular measures of the arcs are $140^{\circ}$ and $220^{\circ}$, and the corresponding angles are $70^{\circ}$ and $110^{\circ}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_845c09db4774ba28be39g-11.jpg?height=343&width=372&top_left_y=160&top_left_x=843)

Answer

$70^{\circ}, 110^{\circ}$.

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