Question

ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is

• A. 90
• B. 180
• C. 45
• D. 30

Answer 1

The Correct Option is A

Given, ∠COD = 120° and ∠BAC = 30°.
As ∠COD = 120°, ∠DAC = 60° (Central angle) 
∠DAC + ∠BAC = 60° + 30° = 90° 
∠A = 90° ⇒ ∠BCD = 90° (Opposite angles are supplementary in a cyclic quadrilateral).