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In the adjoining figure,O is centre of t...

In the adjoining figure,O is centre of the circle , If ` angle ACB= 30^(@), angle ABC=60^(@), angle DAB= 35^(@) and angle DBC=x^(@)`, then the value of x is

A

35

B

40

C

65

D

55

Text Solution

Verified by Experts

The correct Answer is:
D
`angle DBC and angle CAD` are two angles in circles produced by the same are `overset(frown)(CD)` with centre at O.
`:.angleDBC= angle CAD.....(1)`
Now, in `Delta ABC, angle ACB= 30^(@) and angle ABC=60^(@)`
`:.angle BAC=180^(@)- (angle ACB+ angle ABC)`
`=180^(@)-(30^(@)+60^(@))=180^(@)-90^(@)=90^(@)`
Again, `angleDAB=35^(@)=35^(@)` (Given) `:. angleCAD= angle BAC- angle DAB=90^(@)-35^(@)=55^(@)`
`:.` from (1) we get, `angle DBC= angle CAD=55^(@), :. x^(@)=55^(@)`
Hence, `x=55 rArr (d)` is correct
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