ABCD is a quadrilateral inscribed in a circle with centre O. If $∠ C O D = 120$ degrees and $∠ B A C = 30$ degrees, then the value of $∠ B C D$ ( in degrees) is ___

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Solution

Following the conditions of question, we get the figure as:

∠COD = $120^{0}$ (Given)
Then, ∠DAC = $60^{0}$ (Half of ∠COD i.e. $120^{0}$ )
Therefore, ∠BAD = $30^{0} + 60^{0} = 90^{0}$
Hence, ∠BCD = $180^{0}$ - ∠BAD (Opposite angles of a cyclic quadrilateral are supplementary angles).
∠BCD = $180^{0} - 90^{0} = 90^{0}$

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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 ___

Following the conditions of question, we get the figure as: ∠COD = 1200 (Given) Then, ∠DAC = 600 (Half of ∠COD i.e. 1200) Therefore, ∠BAD = 300+600=900 Hence, ∠BCD = 1800 - ∠BAD (Opposite angles of a cyclic quadrilateral are supplementary angles). ∠BCD = 1800–900=900

ABCD is a quadrilateral inscribed in a circle with centre O. If $∠ C O D = 120$ degrees and $∠ B A C = 30$ degrees, then the value of $∠ B C D$ ( in degrees) is ___