In the figure, it is given that $O$ is the centre of the circle and $\angle AOC = 150^o$. Find $\angle ABC$.
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Given:

In the figure, it is given that $O$ is the centre of the circle and $\angle AOC = 150^o$.

To do:

We have to find $\angle ABC$.

Solution:

$\angle AOC + reflex\ \angle AOC = 360^o$

$150^o + reflex\ \angle AOC = 360^o$

 Reflex $\angle AOC = 360^o - 150^o = 210^o$

arc $AEC$ subtends $\angle AOC$ at the centre and $\angle ABC$ at the remaining part of the circle.

Therefore,

Reflex $\angle AOC = 2\angle ABC$

$210^o = 2\angle ABC$

Hence $\angle ABC = \frac{210^o}{2} = 105^o$.

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Updated on: 10-Oct-2022

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