prove that sum of opposite angles of cyclic quadrilateral is 180 degree

Hi!

Here is the proof of the statement provided by you.

 

Consider a cyclic quadrilateral ABCD inscribed a circle with centre at O

In order to prove this theorem, join OB and OD

 

 

⇒∠BAD + ∠BCD = 180°  ... (1)

 

Similarly, by joining OA and OC it can be proved that

∠ABC + ∠ADC = 180°   ... (2)

 

Equation (1) and equation (2) shows that the sum of opposite angles of a cyclic quadrilateral is 180 degree.

 

Hope! This will help you.

Cheers!