Prove that The sum of either pair of opposite angles of a cyclic
quadrilateral is 180º.
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!