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If A B C D is a cyclic quadrilateral i...

If `A B C D` is a cyclic quadrilateral in which `AD|\|BC` . Prove that `/_B=/_C` oved.

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Solution:
`ABCD` is a cyclic quadrilateral
`=>/_B+/_D=180^@` and `/_A+/_C=180^@`Now,
`AD |\| BC`
`=>/_B+/_A=180^@` and `/_C+/_D=180^@`
From `{i}` and `{ii}` , We have
`/_B+/_D+/_B+/_A=360^@`and`/_A+/_C+/_C+/_D=360^@`
`=>2/_B+/_D+/_A=2/_C+/_A+/_D`
`=>/_B=/_C`.
Hence proved.
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