In the given figure, `ABCD` is a cyclic quadrilateral in which `AB` `"||"` `DC`. If`/_ BAD = 100^(@)` , find
`(i) /_ BCD, (ii) /_ ADC, (iii) /_ ABC`.

Explanation

(i) We know that the opposite angles of a cyclic quadrilateral are supplementary.
`:. /_ BAD + /_ BCD = 180^(@)`
`implies 100^(@) + /_BCD = 180^(@)`
`implies /_ BCD = 180^(@) -100^(@) = 80^(@)`
(ii) `AB "||" DC` and `DA` is the transversal.
`:. /_ADC + /_ BAD = 180^(@) ` [sum of int. opp. of `/_ s]`
`implies /_ADC + 100^(@) = 180^(@)`
`implies /_ ADC = 180^(@) - 100^(@) = 80^(@)`
(iii) Using the fact that the opposite angles of a cyclic quadrilateral are supplementary, we have
`/_ ABC + /_ ADC =180^(@)`
`implies /_ ABC + 80^(@) = 180^(@) ` `[ :' /_ADC = 80^(@) ]`
`implies /_ ABC =180^(@) -80^(@) = 100^(@)`
`:. /_ BCD = 80^(@) , /_ ADC = 80^(@)` and `/_ ABC = 100^(@)`