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In quadrilateral A B C D ,\ A O\ a n d\ ...

In quadrilateral `A B C D ,\ A O\ a n d\ B O` are the bisectors of `/_A\ a n d\ /_B` respectively. Prove that `/_A O B=1/2(/_C+/_D)dot`

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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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