Question

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

Answer 1

It is given that O is centre of the circle and ∠BOD = 160°

We have to find the values of x and y.

As we know that the angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Therefore,

Since, quadrilateral ABCD is a cyclic quadrilateral.

So,

x + y = 180° (Sum of opposite angles of a cyclic quadrilateral is 180°.)

Hence and