Question

prove that an exterior angle of a cyclic quadrilateral is congruent to the angle opposite to its adjacent angle​

Answer 1

Step-by-step explanation:

Side DC of cyclic quadrilateral ABCD is produced and point E is taken on it.

To Prove:

∠BCE≃∠BAD

Proof:

∠BCE + ∠BCD=180. (Angles in a linear pair) ...... (1)

∠BAD + ∠BCD=180. (Opposite angles of a cyclic quadrilateral) ...... (2)

From (1) and (2)

∠BCE≃∠BAD

Hence an exterior angle of cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle.