Question

prove sum of opposite angle of cyclic quadrilateral is 180 degress

Answer 1

The sum of the either pair of the opposite angles of a cyclic quadrilateral is 180°. (Angles are supplementary).
Given: Let ABCD be a cyclic quadrilateral
To Proof: The sum of either pair of the opposite angles of a cyclic quadrilateral, is 180°. (Angles are supplementary).
Given: Let ABCD be a cyclic quadrilateral
To Proof: ∠A + ∠C = 180° and ∠B + ∠D = 180°
Construction: Join OB and OD.


Proof:
∠BOD = 2 ∠BAD
∠BAD = ∠BOD
similarly, ∠BCD = ∠DOB
... ∠BAD + ∠BCD= ∠BOD + ∠DOB
= (∠BOD + ∠DOB)
= × 360°
= 180°
Similarly ∠B + ∠D = 180°