In a quadrilateral ABCD, CO and Do are the bisectors of ∠C and ∠D respectively.

In ΔDOC

∠1 + ∠COD + ∠2 = 180°      [Angle sum property of a triangle]

⟹ ∠COD = 180 − (∠1 − ∠2)

⟹ ∠COD = 180 − ∠1 + ∠2

⟹ ∠COD = 180 − [1/2 LC + 1/2 LD]        [∵ OC and OD are bisectors of LC and LD respectively]

⟹ ∠COD = 180 – 1/2(LC + LD)      ... (i)

In quadrilateral ABCD

∠A + ∠B + ∠C + ∠D = 360°  [Angle sum property of quadrilateral]

∠C + ∠D = 360° − (∠A + ∠B)   .... (ii)

Substituting (ii) in (i)

⟹ ∠COD = 180 – 1/2(360 − (∠A + ∠B))

⟹ ∠COD = 180 − 180 +1/2(∠A + ∠B))

⟹ ∠COD = 1/2(∠A + ∠B))