Solution: Because ∠AOC and ∠AOD are complementary and ∠BOD is antipodal angle, ∠ AOD = 180-60 = 120.

And because OE divides ∠AOD equally, then ∠ EOD = 120 ÷ 2 = 60.

Therefore, ∠ doe = ∠ BOD+∠ EOD = 60+60 =120.