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Prove: If a quadrilateral is inscribed in a circle, then an exterior angle of the quadrilateral is congruent to its opposite interior angle. 

 May 4, 2020
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Look  at the following image

 

 

 

 

Let angle EBC  be  the  exterior angle of the quadrilateral

And  the opposite interior angle to  this  is angle ADC

 

We can use  the  fact  that  if a quadrilateral  is insribed in a circle, then oppsite inscribed angles  are supplementary

 

Then

 

angle ABC  +  angle  ADC   =  180

Likewise

angle ABC + angle EBC  =  180 

 

This  implies  that

 

angle ABC  +  angle ADC    =  angle ABC  +  angle EBC

 

Subtract   angle ABC from both sides

 

angle ADC  =  angle EBC 

 

 

cool cool cool 

 May 4, 2020

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