`A B C D` is a cyclic quadrilateral in which `A C\ a n d\ B D` are its diagonals. If `/_D B C=55^0\ a n d\ /_B A C=45^0,` find `/_B C D`

Explanation

In the figure, `ABCD` is a cyclic quadrilateral whose diagonals `AC \and\ BD` are joined.
`/_DBC=55^0 \and\ /_BAC=45^0`
`/_BAC \and\ /_BDC` are in the same segment
`/_BAC=/_BDC=45^0`
Now in `/_\ BCD , /_DBC+/_BDC+/_BCD=180^0`(sum of angles of a triangle)
`55^0+45^0+/_BCD=180^0`
`/_BCD=180^0-100^0=80^0`
Hence,`/_BCD=80^0`