If $O$ is the centre of the circle and $\angle ACB=50^{\circ}$, then find reflex $\angle AOB$.
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Given: In the given figure, a circle with centre $O$ and $\angle ACB=50^{\circ}$.
To do: To find the reflex $\angle AOB$.
Solution:
Here, $AB$ is chord.
As known, angle subtended by chord at the centre of a circle is double of the angle subtended at it's circumference.
$\therefore \angle AOB=2\angle ACB$
$\Rightarrow \angle AOB=50^{\circ}\times2=100^{\circ}$
$\therefore$ Reflex $\angle AOB=360^{\circ}-100^{\circ}=260^{\circ}$
Thus, reflex $\angle AOB=260^{\circ}$.
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