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If the sum of any pair of opposite angles of a quadrilateral is `180^@`; then the quadrilateral is cyclic.

Text Solution

Verified by Experts

Let `ABCD` be a cyclic quadrilateral.
Let us join `OB` and `OD`.
Then, `/_BOD=2/_BCD`
`/_BCD=1/2/_BOD`
Similarly, `/_BAD=1/2/_DOB`
`:./_BAD+/_BCD=1/2/_BOD+1/2+/_DOB`
`=1/2(/_BOD+/_DOB)=1/2xx360^@`
`=180^@`
Similarly, `/_B+/_D=180^@`
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