Question

In fig, D is cyclic quadrilateral in which AC and BD are diagonals. If ∠DBC = 55° and ∠BAC = 45°, then ∠BCD will be :

(A) 80°

(B) 90°

(C) 110°

(D) 115°

Answer 1

Answer is (A) 80°

∠CAD = ∠DBC = 55° (angles of same segment)

∴ ∠DAB = ∠CAD + ∠BAC

55°+ 45° = 110°

But ∠DAB + ∠BCD = 180° (opposite angles of cyclic quadrilateral)

similarly, ∠BCD = 180° – 100° = 80°