In the given figure, O is the centre of the circle. Then, find ∠CBD

In the given figure, O is the centre of the circle. Then, find ∠CBD.
image

We know that the angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Then, ∠AOC=2∠APC
=>∠APC = 1/2 ∠AOC = 1/2 x 100° = 50°
Now, ∠APC + ∠ABC = 180°
[∵ sum of opposite angles of a cyclic quadrilateral is 180°]
=> 50° +∠ABC = 180°
=∠ABC = 180°- 50° = 130°
Also,∠ABC + ∠CBD = 180° [linear pair axiom]
=> 130° +∠CBD =180°
=>∠CBD = 180° - 130° = 50°