Question

prove that the exterior angle at one vertex and interior opposite angle of a cyclic quadrilateral are equal​

Answer 1

Answer:

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

To prove : ∠CBE = ∠ADC

Proof :

∠ABC + ∠ADC = 180° [Opposite angles of cyclic quadrilateral.]...........(1)

∠ABC + ∠CBE = 180° [Linear Pair angles.]........(2)

[From equation (1) and (2)

∠ABC + ∠ADC = ∠ABC + ∠CBE

∠ADC = ∠CBE

Hence proved.