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ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC = 30°, find ∠BCD. Further, if AB = BC, find ∠ECD. |
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Answer» ∠DBC = 70°, ∠BAC = 30°, then ∠BCD =? AB = BC, then ∠ECD = ? ∠DAC and ∠DBC are angles in same segment. ∴ ∠DAC = ∠DBC = 70° ∴ ∠DAC = 70° ABCD is a cyclic quadrilateral. ∴ Sum of opposite angles is 180°. ∠DAB + ∠DCB = 180 100 + ∠DCB = 180 [∵ ∠DAC + ∠BAC = ∠DAB 70 + 30 = 100] ∠DCB = 180 – 100 ∴ ∠DCB = 80 ∠DCB = ∠BCD = 80 ∴ ∠BCD = 80 In ∆ABC, AB = AC, ∴ ∠BAC = ∠BCA = 30° ∠BCA = 30° ∠ECD = ∠BCD – ∠BCA = 80 – 30 ∴ ∠ECD = 50°. |
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