Question

An exterior angle of a cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle.
write the proof of the theorem yourself.

Answer 1

To prove

angle CBE = angle ADC

Proof

ABCD is a cyclic quadrilateral.

So

angle ABC+ angleADC = 180 (opp.angle of cyclic quadrilateral)

angle ABC+ angle CBE= 180( Linear pair)

from above

angle ABC+ angle ADC = angleABC + angle CBE

Or

angle ADC = angle CBE

here is your answer.

hope it may help you

Answer 2

Answer:

Step-by-step explanation:

To prove  :

Let O be the centre of the circle.  Join O to B and D.  Then let the angle subtended by the minor arc and the major arc at the centre be xº and yº respectively.angle CBE = angle ADC

Proof :

ABCD is a cyclic quadrilateral.

So

angle ABC + angleADC = 180          ...(opp.angle of cyclic quadrilateral)

angle ABC+ angle CBE= 180             ...( Linear pair)

from above

angle ABC+ angle ADC = angleABC + angle CBE

Or

angle ADC = angle CBE

Hence proved