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Question
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° `
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