Prove: If a quadrilateral is inscribed in a circle, then an exterior angle of the quadrilateral is congruent to its opposite interior angle.
+128475 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
