in a quadrilateral ABCD, AOand BOare bisectors for angle A and angle B respectively. prove that Angle AOB = 1/2 ( angle C + angleD)
pllz help me out meritnation experts!
Given, AO and BO are the bisectors of angle A and angle B respectively.
∴ ∠1 = ∠4 and ∠3 = ∠5 ... (1)
To prove: ∠2 = 
(∠C + ∠D)
Proof:
In quadrilateral ABCD
∠A + ∠B + ∠C + ∠D = 360°
(∠A + ∠B + ∠C + ∠D) = 180° ... (2)
Now in ΔAOB
∠1 + ∠2 + ∠3 = 180° ... (3)
equating (2) and (3), we get
∠1 + ∠2 + ∠3 = 
∠A + ∠B + (∠C + ∠D)
∠1 + ∠2 + ∠3 = ∠1 + ∠3 + (∠C + ∠D)
∴ ∠2 = 
[∠C + ∠D]
Hence proved !!