In Fig. 16.181, O is the centre of the circle. Find ∠ CBD .

Question

In Fig. 16.181, O is the centre of the circle. Find &#x2220; CBD .

Philoid · Accepted Answer

Given that,

∠BOC = 100^o

By degree measure theorem,

∠AOC = 2 ∠APC

100^o = 2 ∠APC

∠APC = 50^o

Therefore,

∠APC + ∠ABC = 180^o (Opposite angles of a cyclic quadrilateral)

50^o + ∠ABC = 180^o

∠ABC = 130^o

Therefore,

∠ABC + ∠CBD = 180^o (Linear pair)

130^o + ∠CBD = 180^o

∠CBD = 50^o