ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC=80∘,∠BAC is 40∘, find ∠BCD.
60∘
∠BAC=40∘ and ∠DBC=80∘
∠BDC=∠BAC [Angles formed by the same segment are equal]
∠BDC=40∘
In ΔBDC,
∠BDC+∠DBC+∠BCD=180∘ [Sum of angles in triangle]
40∘+80∘+∠BCD=180∘
∠BCD=180∘−120∘
∠BCD=60∘