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Question

In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If DBC=55 and BAC=45, then BCD = ___ .

A
80
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B
70
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C
60
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D
90
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Solution

The correct option is A 80
Note that CAD=DBC=55. (Angles in the same segment)
Thus, DAB=CAD+BAC=55+45=100.
But, DAB+BCD=180. (Opposite angles of the cyclic quadrilateral ABCD)
So, BCD=180100=80.

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