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In Fig 10.33, ABCD is a cyclic quadrila...

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

Text Solution

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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^@`
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