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The sides AB and DC of a cyclic quadrila...

The sides `AB` and `DC` of a cyclic quadrilateral `ABCD` when produced meet at `E` and the sides `DA` and `CB` when produced meet at `F.` Given `angle BEC=38^(@)`,`angle BAD=102^(@)`. Find the values of `angle AFB` and `angle ADC`.

Text Solution

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In `Delta ADE`,
`angle ADE = 180^@-(angle AED+angle EAD)`
`=180^@-(38^@+102^@)`
`= 180^@-140^@`
`40^@`
`rArrangleADC=40^@`
square `ABCD` is a cyclic quadrilateral.
`thereforeangleDCB+angleDAB=180^@`
`rArrangle DCB=180^@-angle DAB`
`=180^@-102^@`
`78^@`
`DeltaDFC`,
`angle DFC=180^@(angle FDC+angle FCD)`
`=180^@-(40^@+78^@)`
`=180^@-118^@`
`62^@`
`angleAFB =62^@` and `angle ADC=40^@`.
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