In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that `/_ ADC = 95^(@)` and `/_ ECF = 20^(@)`. The, `/_ BAD = ?`

Options

A. `95^(@)`
B. `85^(@)`
C. `105^(@)`
D. `75^(@)`

Answer

C

Explanation

`/_ ABC + /_ ADC = 180^(@) implies /_ ABC + 95^(@) = 180^(@) implies /_ABC = 85^(@)`
Now, `VF||AB ` and CB is the transversal
`:. /_ BCF = /_ ABC = 85^(@)` [alt. int. `/_ s]`
`implies /_ BCE = 85^(@)+ 20^(@) = 105^(@)`
`implies /_ DCB = 180^(@) - 105^(@) = 75^(@) `
Now, /`_ BAD + /_ BCD = 180^(@) implies /_ BAD + 75^(@) = 180^(@) implies /_ BAD = 105^(@)`