Question

proof :if a sum of either pair of opposite angles of cyclic quadrilateral is 180°

Answer 1

Answer:

Step-by-step explanation:

Theorem 7: 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 (Fig.) To Proof: The sum of either pair of the opposite angles of a cyclic quadrilateral, is 180°

Answer 2

Hi Sister. Here is your proof☺

Sol : Given : Let ABCD is cyclic quadrilateral

. To prove : ∠A + ∠C = 180°  and ∠B + ∠D = 180°. 

Construction : join OB and OD.  

Proof : ∠BOD = 2 ∠BAD     

∠BAD = 1/2∠ BOD

Similarly ∠BCD = 1/2 ∠DOB 

∠BAD + ∠BCD =

1/2∠BOD + 1/2 ∠DOB                  

=1/2(∠ BOD + ∠DOB)                  

= (1/2)X360° = 180° 

Similarly ∠B + ∠D = 180°

❤hope it helps you ❤