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We know angle A+angle B +angle C+ angle D=360              (1)
In triangle ABO  angle AOB+ 1/2(angle A+angle B)=180                                      
                                    2(AOB+ 1/2(angle A+angle B)=360      (2)
We have  angle   2 AOB + angle A+ angle B = angle A + angle B +angle C+ angle D
                 This gives                       angle AOB= (angle C + angle D)/2
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