Short Note

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

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#### Solution

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,

`x = 1/2 (160°)`

= 80°

Since, quadrilateral *ABCD* is a cyclic quadrilateral.

So,

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

` y = 180° - x`

=180° - 80°

= 100°

Hence `angle = 100° ` and `anglex = 80° `

Is there an error in this question or solution?

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