Q2 of 33 Page 57

Prove that any exterior angle of a cyclic quadrilateral is equal to the interior angle at the opposite vertex.



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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