Question

In a cyclik quadrilateral ABCD , AO,BO,MC,DM are the bisector of angle A ,angle B,angleC,angleD respectively prove that angle CMD+angleAOB=180

Answer 1

Answer:

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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