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

In the adjoining figure, O is the centre of circle. If `angle BCD=28^(@), angle AEC= 38^(@)`, then the value of `angle AXB` is-

A

`56^(@)`

B

`94^(@)`

C

`38^(@)`

D

`28^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
In the circle with centre at O, the angles ` angle BAD and angle BCD` are both angles in circle produced by the are `overset(frown)(BD)`.
`:. angle BAD= angle BCD=28^(@)` (Given )[ by theorem-35]
Again `angle AEC=38^(@), :. ADC= angle AEC+ angle DAB)`
`[ :.` external `angle ADC` = internally opposite `(angle AEC + angle DAE]`
`:.angleADC=38^(@)+ angleBAD[ :. angle DAB and angle BAD` are same angles]
`=38^(@)+28^(@)=66^(@)`
Again`angle AXB`= internally opposite `(angle XDC+ angle XCD)`
`= angle ADC+ angle BCD=66^(@)+28^(@)=94^(@)`
Hence (b) is correct.
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