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In the adjoining firgure, O is the centr...

In the adjoining firgure, O is the centre of the circle, if `angle BAD=65^(@), angle BDC=45^(@)` then the value of `angle CBD` is

A

`65^(@)`

B

`45^(@)`

C

`40^(@)`

D

`20^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
`angle BAC= angle BDC= 45^(@) [ :. angle BDC=45^(@)` (Given)]
Again, `angle BAD=65^(@)` (Given) `:. angleCAD= angleBAD- angle BAC= 65^(@)-45^(@)=20^(@)`
Now, both `angle CAD and angleCBD` are angles in circle produced by the same are `overset(frown)(CD)` of the circle.
`:. angle CAD= angle CBD`
But `angle CAD=20^(@), :. angle CBD=20^(@)`
Hence (d) is correct
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