In the given figure, O is the centre of a circle `/_ AOC = 110^(@)` and side AB has been produced to a point D. Find `/_ CBD`.

Explanation

Take a point E on the remaining part of the circumference . Join EA and EC.
We know that the angle subtended by an arc at the centre of a circle is twice the angle subtended at a point on the remaining part of the circumference.
`:. /_ AEC = (1)/(2) /_ AOC = ((1)/(2) xx 110^(@)) = 55^(@)`
Now, ABCE is a cyclic quadrilateral whose side AB has been produced to a point D.
But, the exterior angle of a cyclic quadrialteral is equal to its interior opposite angle.
`:. /_ CBD =/_ AEC = 55^(@)`
Hence, `/_ CBD = 55^(@)`