Theorem : If one side of a cyclic quadrilateral is produced, then the exterior angle is equal to the interior opposite angle.
Given : A cyclic quadrilateral ABCD. Side AB is produced to E to form the exterior angle ∠CBE.
To Prove : ∠ADC=∠CBE
Proof :
∠1+∠2=180°— (1) (Opposite angles of cylic quadrilateral are supplemntary)
∠2+∠3=180°— (2) (Linear Pair)
From equation (1) and (2)
⇒ ∠1+∠2=∠2+∠3
∠1=∠3
∠ADC=∠CBE
Hence Proved ■
Practice Question :
If an exterior angle of a cyclic quadrilateral is 50°, then the opposite interior angle is :
(A) 130°
(B) 40°
(C) 50°
(D) 90°