In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55∘ and ∠BAC=45∘, then ∠BCD = ___ .
A
80∘
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
70∘
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
60∘
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
90∘
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A80∘ Note that ∠CAD=∠DBC=55∘. (Angles in the same segment) Thus, ∠DAB=∠CAD+∠BAC=55∘+45∘=100∘. But, ∠DAB+∠BCD=180∘. (Opposite angles of the cyclic quadrilateral ABCD) So, ∠BCD=180∘–100∘=80∘.