Question

prove it ques no 10 sum of

Answer 1

Given: Let ABCD be a cyclic quadrilateral (Fig.)
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 (Fig.)
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°