In the adjoining figure, O is the centre of the circle. If `angle AEB=110^(@), angle CBE=30^(@)`, then the value of `angle ADB` is

Options

A. `70^(@)`
B. `60^(@)`
C. `80^(@)`
D. `90^(@)`

Answer

C

Explanation

In the circle with centre at O, the angle in circle produced by the are `overset(frown)(AB) "are" angle ADB and angle ACB`.
`:. angleADB= angleACB` [ by theorem-35] ......(1)
Now , if the side CE of `Delta BCE` be produced to A, then the external angle `angle AEB` produced is equal to the internally opposite `( angle CBE+ angle BCE)`, i.e.,
`angle AEB= angle CBE+ angleBCE`
or, `110^(@)= angle CBE+ angle BCE [ :. angle AEB=110^(@)` (Given)]
`or, angleBCE= 110^(@)- angle CBE`
`or, angle BCE=110^(@)-30^(@) [ :. angle CBE= 30^(@)` (Given)]
`or, angle ACB=80^(@) [ :. angle BCE and angle ACB` are same angles]
`:. angle ADB= angle ACB=80^(@)` [ from (1)]
`or, angle ADB= 80^(@) rArr(c) ` is correct