ABCD is a cyclic quadrilateral whose diagonals interest at E. If angle DBC = 70 , angle BAC=30

find angle BCD. Further, if AB=BC, find angleECD.

 angle bac = angle bdc = 30 degrees (angles in the same segment)

now in triangle BDC by angle sum property

angle bcd=80 degrees

when ab=bc so by (angles opoposite equal sides )

angle bac=angle bca= 30 degrees

now, bcd=bca+acd

80 degrees=30 degrees+ angle acd

so angle acd=50 degrees

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