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Q.
In the given figure, ${ }^{\prime} O ^{\prime}$ is the centre of the circle and $\angle ABC =40^{\circ}$. Determine the measure of reflex $\angle AOC$
Geometry
Solution:
Given, $\angle ABC =40^{\circ}$.
An angle subtended by an arc at the centre of the circle is double the angle subtended
by the same arc at any point on the remaining part of the circle.
$\angle AOC =2 \angle ABC =80^{\circ} $
$\therefore \text { Reflex } \angle AOC $
$=360^{\circ}-80^{\circ}=280^{\circ}$
