Question

Prove that "An exterior angle of cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle."

Answer 1

Given: Side DC of cyclic quadrilateral ABCD is produced and point E is taken on it.
To Prove: $\angle BCE\simeq \angle BAD$
Proof: $\angle BCE+\angle BCD={180}^o$
(Angles in a linear pair) ...... (1)
$\angle BAD+\angle BCD={180}^o$
(Opposite angles of a cyclic quadrilateral) ...... (2)
From (1) and (2)
$\angle BCE\simeq \angle BAD$
Hence an exterior angle of cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle.