∠EOC=2∠BOE is the angular bisector of OB ∠EOC.

Because < AOB+< BOC = 180.

Then DOB = (180-∠ BOC)/2 = 90-∠ BOC/2.

Because ∠ DOE = ∠ DOB-∠ EOB = 72 = 90-∠ BOC/2-∠ EOB = 72.

If 3∠EOB/2= 18, then ∠ EOB = 12.

Then < EOC = 2 < BOE = 24.