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The side AB of the cyclic quadrilateral ...

The side AB of the cyclic quadrilateral ABCD is extended to X . If `angleXBC=82^(@)and angleADB=47^(@)` Find the value of `angleBAC`.

Text Solution

Verified by Experts

Given that `angleXBC=82^(@)`
`thereforeangleABC=180^(@)-angleXBC=180^(@)-82^(@)=98^(@)`
Again , two angles in circle produced by the arc AB are `angleADBandangleACB, thereforeangleADB=angleACB,thereforeangleACB=47^(@)` ,
Now in `DeltaABC,angleBAC+angleACB+angleABC=180^(@)`
or , `angleBAC+47^(@)+98^(@)=180^(@)" or "angleBAC=180^(@)-145^(@)=35^(@)`
Hence `angleBAC=35^(@)`
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