In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If `/_ DBC = 70^(@)` and `/_ BAC = 30^(@)` , find `/_ BCD` . Further, if AB `=` BC , find `/_ ECD`

Explanation

We have
`/_ BDC = /_ BAC = 30^(@)` [angles in the same segment ]
Now , in `Delta BCD` , have
`/_ DBC + /_ BCD + /_ BDC = 180^(@)`
`[ :' ` sum of the angles of a `Delta ` is `180^(@)` ]
`implies 70^(@) + /_ BCD + 30^(@) = 180^(@)`
`implies /_BCD = 180^(@) - 100^(@) = 80^(@)`
Now,AB= BC `implies /_ BCA = /_ BAC = 30^(@)`
`:. /_ ECD = /_ BCD - /_ BCA = 80^(@) - 30^(@) = 50^(@)`