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Questions
In the given figure, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.
In the following figure, ABCD is a cyclic quadrilateral. If ∠DBC = 55° and ∠BAC = 45°, find ∠BCD.
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Solution
We have to find ∠BCD
Since angles in the same segment of a circle are equal
So ∠CAD = ∠DBC = 55°.
∠DAB = ∠CAD + angle BAC
= 55° + 45°
= 100°
Since ∠DAB + ∠BCD = 180° ...(opposite angles of cyclic quadrilateral)
∠BCD = 180° − 100°
= 80°
Hence ∠BCD = 80°
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