Question

In Fig.  ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.

Answer 1

Since angles on the same segment of a circle are equal 

Therefore, 

∠CAD = ∠DBC = 55° 

∠DAB = ∠CAD + ∠BAC 

= 55° + 45° = 100° 

But, 

∠DAB + ∠BCD = 180° 

(Opposite angles of a cyclic quadrilateral) 

Therefore, 

∠BCD = 180° – 100° 

∠BCD = 80°