Question

prove that sum of either pair of opposite angles of a cyclic quadrilateral is supplementary angle ​

Answer 1

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

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Answer 2

Answer:

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Step-by-step explanation: