Question

In following fig., O is the centre of the circle. Find ∠ CBD. 

Answer 1

It is given that ∠ AOC = 100° 

Arc AC subtends ∠ AOC at the centre of circle and ∠ APC on the circumference of the circle

∴  ∠ AOC = 2 c

⇒ ∠ APC = `(100°)/2` = 50°

It can be seen that APCB is a cyclic quadriIateral. 

∴ ∠ APC + ∠ ABC = 180°  (Sum of opposite angles of a cyclic quadrilateral)

⇒ ∠ ABC = 180° - 50° = 130°

Now , ∠ ABC + ∠ CBD = 180°   (Linear pair angles)

∠ CBD = 180° - 130° = 50°