Question

in a quadrilateral ABCD ,AO and BOI bisector of angle A and Angle B respectively prove that angle aob is equal to half (angle A + Angle B)

Answer 1

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