If a side of a cyclic quadrilateral is produced, then prove that the exterior angle is equal to the interior opposite angle. [3 MARKS]
Concept: 1 Mark
Application: 2 Marks
Given: A cyclic quadrilateral ABCD. Side AB is produced to E
To prove: ∠CBE=∠ADC
Proof : ∠ABC+∠ADC=180∘ .......... (i)
[sum of opposite pairs of angles in a cyclic quadrilateral.]
But ∠ABC+∠CBE=180∘ ............. (ii)
[ ∠ABC and ∠CBE are linear pairs]
From (i) and (ii)
∠ABC+∠ADC=∠ABC+∠CBE
∠ADC=∠CBE
or ∠CBE=∠ADC