In Figure, `O` is the centre of the circle and `/_D A B=50^0dot` Calculate the values of `x\ a n d\ y`

Explanation

It is given that `O` is the centre of the circle
`/_DAB=50^0`

We know that the radii of the circle are equal
`OA=OB`
`/_OAB+/_OBA+/_AOB=180^0`
`50^0+50^0+/_AOB=180^0`
`/_AOB=80^0`
`x=180^0-80^0=100^0`
We know that the opposite angles of a cyclic quadrilateral are supplementary
`/_DAB+/_BCD=180^0`
`50^0+/_BCD=180^0`
`/_BCD=180^0-50^0=130^0=y`
Therefore the value of `x \is\ 100^0 \and\ y is 130^0`
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