(i) Say,

∠FOE = x

∠DOE = y

∠BOC = z

∠AOF + 30^o = 180^o (∠AOF + ∠FOG = 180^o)

∠AOF = 150^o

∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOF = 150^o

30^o + z + 30^o + y + x = 150^o

x + y + z = 90^o(i)

Now,

∠FOC = 90^o

∠FOE + ∠EOD + ∠DOC = 90^o

x + y + 30^o = 90^o

x + y = 60^o (ii)

Using (ii) in (i), we get

x + y + z = 90^o

60^o + z = 90^o

z = 30^o (∠BOC = 30^o)

∠BOE = 90^o

∠BOC + ∠COD + ∠DOE = 90^o

30^o + 30^o + ∠DOE = 90^o

∠DOE = 30^o

Now, we have

x + y = 60^o

y = 30^o

∠FOE = 30^o

(ii) Right angles are:

∠DOG, ∠COF, ∠BOF, ∠AOD

(iii) Three pairs of adjacent complimentary angles are:

∠AOB, ∠BOD

∠AOC, ∠COD

∠BOC, ∠COE

(iv) Three pairs of adjacent supplementary angles are:

∠AOB, ∠BOG

∠AOC, ∠COG

∠AOD, ∠DOG

(v) Three pairs of adjacent angles are:

∠BOC, ∠COD

∠COD, ∠DOE

∠DOE, ∠EOF