In Fig. 16.178, O is the centre of the circle. If ∠BOD=160°, find the values of x and y.

Question

In Fig. 16.178, O is the centre of the circle. If &#x2220; BOD =160&#xB0;, find the values of x and y .

Philoid · Accepted Answer

Given that,

O is the centre of the circle

We have,

∠BOD = 160^o

By degree measure theorem,

∠BOD = 2 ∠BCD

160^o = 2x

x = 80^o

Therefore,

∠BAD + ∠BCD = 180^o (Opposite angles of Cyclic quadrilateral)

y + x = 180^o

y + 80^o = 180^o

y = 100^o