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In a quadrilateral ABCD, AO and BO are t...

In a quadrilateral ABCD, AO and BO are the bisectors of `angleA and angleB` respectively. Prove that `angleAOB=1/2(angleC+angleD).`

Text Solution

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In`DeltaDeltaOB+angle1+angle2=180^(@)`
`implies" "angleAOB=180^(@)-(angle1+angle2)`
`implies" "angleAOB=180^(@)-((angleA)/(2)+(angleB)/(2))`
`implies" "angleAOB=180^(@)-1/2[360^(@)-(angleC+angleD)](because angleA+angleB+angleC +angleD=360^(@))`
`implies" "angleAOB=180^(@)-180^(@)+1/2(angleC+angleD)`
`implies" "angleAOB=1/2(angleC+angleD)`
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