In the given figure, O is the centre of a circle and `/_ AOC = 140^(@)` . Find `/_ ABC`

Explanation

Take a point D on the remaining part of the circumference. Join DA and DC, as show in th e figure.
We know that the angle at the centre of a circleis twice the angle at any point on the remaining part of the circumference.
`:. /_ADC = (1)/(2) /_ AOC = ((1)/(2) xx 140^(@))= 70^(@)`

We know that the possible angles of a cyclic quadrilateral supplementary.
`:. ` from cyclic quadrilateral ABCD, we have
`/_ ABC + /_ ADC = 180^(@)`
`implies /_ ABC + 70^(@) = 180^(@) `
`implies /_ ABC = 180^(@) - 70^(@) = 110^(@)`