Question

In quadrilateral ABCD, AO and BO are bisectors of Angle A and B respectively prove that Angle AOB is half of( Angle C +Angle D)

Answer 1

a/c
angle OAB=1/2DAB-------(1)
OBC=1/2CBA--------(2)

we know quadiratral ABCD

A+B+C+D=360
A+B=360-(C+D)---------(3)

now
triangle AOB
angle AOB=180-(OAB+OBC)
from equation (1) and (2)
AOB=180-1/2(DAB+CBA)
=180-1/2 (A+B)
from equation (3)
AOB=180-1/2 {360-(C+D)}=1/2(C+D)
so,
angle AOB=1/2 (angle C+angle D)