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In the adjoining figure , the diagonals ...

In the adjoining figure , the diagonals of the cyxlic quadrilateral PQRS intersect each other at the point X in such a way that `anglePRS=65^(@) andangleROS=45^(@)`. Find the values of `angleSQP and angleRSP` .

Text Solution

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Two angles in circle produced by the arc PS are ` anglePRSandanglePQS` .
`thereforeanglePQS=anglePRS=65^(@)thereforeangleSQP=65^(@)`
Again , two angles in circle produced by the arc RS are `angleRQSandangleRPS`
`thereforeangleRQS=angleRPSrArrangleRPS=45^(@)[becauseangleRQS=45^(@)]`
Then in `DeltaPRS,angleRSP+anglePRS+angleRPS=180^(@)`
or, `angleRSP^(@)+65^(@)+45^(@)=180^(@)[becauseangleRPS=45^(@)]`
or, `angleRSP=180^(@)-110^(@)=70^(@)`
`thereforeangleSQP=65^(@)andangleRSP=70^(@)`
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