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Question

Quantitative Aptitude Question on Quadrilaterals

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

90

Explanation

Solution

Opposite angles are supplementary in a cyclic quadrilateral

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).