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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]


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Solution

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


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