Question

ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If angle DBC = 55° and angle BAC = 45° and AD = AB. Find angle ADC​

Answer 1

given that ∠CAD = ∠DBC = 55 (Since angles in the same segment)
∠DAB = ∠CAD + ∠BAC
= 55 + 45
= 100
similarly ∠DAB + ∠BCD = 180 (Opposite angle of a cyclic quadilateral)
=> ∠BCD = 180 - ∠DAB
= 180 - 100
=> ∠BCD = 80




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