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In the adjoining figure, ABCD is a cycli...

In the adjoining figure, ABCD is a cyclic quadrilateral. BA is produced to F.If AE||CD, `angleABC=92^(@)andangleFAE=20^(@)` , then the value of `angleBCD` is

A

`20^(@)`

B

`88^(@)`

C

`108^(@)`

D

`72^(@)`

Text Solution

Verified by Experts

ABCD is a cyclic quadrilateral.
`thereforeangleABC+angleADC=180^(@)`
or , `92^(@)+angleADC=180^(@)[becauseangleABC=92^(@)]`
or, `angleADC=180^(@)-92^(@)=88^(@)`
Also given that AE||CD and AD is their tranversal.
`thereforeangleCDA="alternate"angleDAE`
or, `88^(@)=angleDAE[becauseangleCDA=88^(@)] thereforeangleDAE=88^(@)`
`thereforeangleDAF=angleDAE+angleEAF=88^(@)+20^(@)[becauseangleDAE=88^(@)]=180^(@)`
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