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Question
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.
Solution
It is given that ABCD is a cyclic quadrilateral with AC and DB as its diagonals.
We have to find `angleBCD`
Since angles in the same segment of a circle are equal
So `angleCAD = angle DBC = 55°`
`angleDAB = angleCAD + angle BAC `
= 55° + 45 °
= 100°
Since `angleDAB + angle BCD = 180°` (Opposite angle of cyclic quadrilateral)
`angleBCD ` = 180° - 100°
= 80°
Hence `angle BCD = 80°`
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