Question

In a quadrilateral ABCD AO and bo are the bisector of angle A and Angle B respectively prove that angle aob is equals to half of angle C plus half of angle d

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