Prove theorem 10.11 of class 9th NCERT chapter 10 i.e.->
The sum of either pair of opposite angles of a cyclic quadrilateral is 180°
Please answer as soon as possible ♡♡♡♡
Answers
Hence The sum of either pair of opposite angles of a cyclic quadrilateral is 180°
Step-by-step explanation:
Let say ABCD is a cyclic Quadrilateral
Then Let say BC is chord and O is center
=> ∠BAD = (1/2)∠BOD ( Minor) ( Angle subtended by chord at center & arc)
∠BCD = (1/2)∠BOD (Major)
Minor & Major can interchange
Adding both
∠BAD + ∠BCD = (1/2)∠BOD ( Minor) + (1/2)∠BOD (Major)
=> ∠BAD + ∠BCD = (1/2) (∠BOD ( Minor) + ∠BOD (Major) )
=> ∠BAD + ∠BCD = (1/2) 360°
=> ∠BAD + ∠BCD = 180°
Similarly taking AC as chord
we can show that
∠ABC + ∠ADC = 180°
Hence The sum of either pair of opposite angles of a cyclic quadrilateral is 180°
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I hope this is helpfull.
