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.

For chordCD,∠CBD=∠CAD...Angles in same segment∠CAD=70°∠BAD=∠BAC+∠CAD=30°+70°=100°∠BCD+∠BAD=180°...Opposite angles of a cyclic quadrilateral⇒∠BCD+100°=180°⇒∠BCD=80°In△ABCAB=BC(given)∠BCA=∠CAB...Angles opposite to equal sides of a triangle∠BCA=30°Also,∠BCD=80°∠BCA+∠ACD=80°⇒30°+∠ACD=80°∠ACD=50°∠ECD=50°