Question

If a side of a cyclic quadrilateral is produced, then prove that the exterior angle is equal to the interior opposite angle. [3 MARKS]

Answer 1

Concept: 1 Mark
Proof: 2 Marks

Given: A cyclic quadrilateral ABCD. Side AB is produced to E

To prove: $\angle CBE=\angle ADC$

Proof : $\angle ABC+\angle ADC={180}^{\circ }$ .......... (i)

[sum of opposite pairs of angles in a cyclic quadrilateral is equal to ${180}^{\circ }$.]

But $\angle ABC+\angle CBE={180}^{\circ }$ ............. (ii)

[ $\angle ABC$ and $\angle CBE$ are linear pairs]

From (i) and (ii)

$\angle ABC+\angle ADC=\angle ABC+\angle CBE$

$\angle ADC=\angle CBE$

or $\angle CBE=\angle ADC$