Prove that

Given, ∠AOC and ∠BOC are supplementary angles

OE is the bisector of ∠BOC and

OD is the bisector of ∠AOC

Therefore, ∠1 = ∠2 and ∠3 = ∠ 4 ________________ (i)

∠BOC + ∠AOC = 180° [Because AOB is a straight line]

⇒ ∠1 + ∠2 + ∠3 + ∠4 = 180°

⇒ ∠1 + ∠1 + ∠3 + ∠3 = 180° [From equation (i)]

⇒ 2 ∠1 +2 ∠3 = 180°

⇒ 2(∠1 + ∠3) = 180°

⇒ ∠1 + ∠3 = 90°

Hence, ∠EOD = 90° proved.