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Question

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If DBC=70, BAC is 30, find BCD. Further if AB=BC, find ECD .
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Solution

DBC=70o,BAC=30o, then BCD=?
AB=BC, then ECD=?
DAC and DBC are angles in same segment
DAC=DBC=70o
DAC=70o
DAC+BAC=70+30=100
ABCD is a cyclic quadrilateral
Sum of opposite angles is 180o
100+DCB=180
[DAC+BAC=DAB=100]
DCB=180100
DCB=80
DCB=BCD=80
BCD=80
In ABC,AB=AC
BAC=BCA=30o
BCA=30o
ECD=BCDBCA=8030
ECD=50o

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