Mathematics
In the given figure, ∠ABC and ∠DBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 40°. Then, ∠BCD = ?
60°
40°
100°
80°
Answer
Given,
Points A and D are on the circle, and both form angles with the chord BC.
∠BDC = ∠BAC = 60° [Angles in same segment are equal]
In ΔBCD,
By angle sum property of triangle,
∠BCD + ∠DBC + ∠BDC = 180°
∠BCD = 180° - ∠DBC - ∠BDC
∠BCD = 180° - 40° - 60°
∠BCD = 80°.
Hence, option 4 is the correct option.
Related Questions
In the given figure, O is the centre of the circle and ∠ACB = 30°. Then, ∠AOB = ?
15°
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In the given figure, O is the centre of the circle. If ∠OAB = 35° and C is a point on the circle, then ∠ACB = ?
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In the given figure, O is the centre of the circle. If ∠OAC = 55°, then ∠OBD = ?
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70°
In the given figure, O is the centre of the circle in which ∠OBA = 30° and ∠OCA = 40°. Then, ∠BOC = ?
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