In Fig 10.33, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If `/_D B C\ =\ 55o`and `\ /_B A C\ =\ 45o`, find BCD

Explanation

We create a figure with the given details.

We are given,

`/_BAC = 45^@ and /_DBC = 55^@`

We know, angles subtended by a common chord are always equal at any point of the circle.

So,`/_CAD=/_DBC = 55^@`

`/_BAD = /_CAD+/_BAC = 55+45 = 100^@`

We know, sum of opposite angles of a cyclic quadrilaterl is `180^@`.

`/_BAD+/_BCD = 180=>/_BCD = 180-100 =80^@`