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An exterior angle of a cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle

Given: ABCD is a cyclic quadrilateral. 

∠BCE is the exterior angle of ABCD. 

To prove: ∠BCE ≅ ∠BAD

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Proof: 

∠BCE + ∠BCD = 180°…… (i) [Angles in a linear pair] 

⟂ABCD is a cyclic quadrilateral. [Given] 

∠BAD + ∠BCD = 180°………. (ii) [Opposite angles of a cyclic quadrilateral are supplementary] 

∴ ∠BCE + ∠BCD = ∠BAD + ∠BCD [From (i) and (ii)] 

∴ ∠BCE = ∠B

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