Question

In the given figure, it is given that O is the centre of the circle and ∠AOC = 150°. Find ∠ABC.

 

Answer 1

It is given that O is the centre of circle and A, B and C are points on circumference.

`angle AOC = 150°`  (Given)

We have to find ∠ABC

The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

\[\angle ABC = \frac{1}{2}\left( \text{ reflex } \angle AOC \right)\]
\[ = \frac{1}{2}\left( 360° - 150° \right)\]
\[ = \frac{1}{2} \times 210° \]
\[ = 105° \]

Hence,`angle ABC = 105°`