Answer :

Given : A cyclic quadrilateral ABCD one of whose side AB is produced to E.

Prove that : ∠CBE = ∠ADC

Proof:

∠ ABC + ∠ ADC = 180° [Opposite angles of cyclic quadrilateral]

∠ ABC + ∠ CBE = 180° [Linear Pair angles.]

∠ABC + ∠ADC = ∠ABC + ∠CBE [From the above equations,]

∠ADC = ∠CBE [Subtraction property]

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