In the figure, ∠ AOF and ∠ FOG form a linear pair. ∠ EOB =∠ FOC = 90° and ∠ DOC = ∠ FOG = ∠ AOB = 30°.
         
Find the measure of ∠ FOE, ∠ COB and ∠ DOE.
       
     

∠ AOF  + ∠ FOG = 180° [Linear pair axiom]
⇒ ∠ AOG = 180°
⇒ ∠ AOB + ∠ EOB + ∠ FOE + ∠ FOG = 180°
30° +90° + ∠ FOE+∠ FOG  = 180°
⇒ ∠ FOE + ∠ FOG = 180° - (30° + 90° )
                                =  180° - 120°
                                =  60°
⇒ ∠ FOE + 30° = 60° [∠ FOG =30° ]
∴ ∠ FOE = 30°
∠ AOB + ∠ EOB + ∠ FOE + ∠ FOG = 180°
⇒ ∠ AOB + ∠ BOC + ∠ COF + ∠ FOG = 180°
⇒ 30° + ∠ BOC + 90° + 30° = 180° [∠ AOB = 30° , ∠ COF = 90° and ∠ FOG = 30° ]
⇒ ∠ BOC = 180° - (30° + 90° + 30° )
              = 180° - 150°
              = 30° ∴ ∠ COB = 30° ……………….(i)
∠ EOB = 90° [Given]
⇒ ∠ BOC + ∠ COD + ∠ DOE = 90°
⇒ 30° + 30° + ∠ DOE = 90° [∠ BOC = 30° from (i) and ∠ COD = 30° , Given]
⇒ ∠ DOE = 90° - (30° + 30° )
              = 90° - 60°
              = 30°
∴ ∠ DOE = 30° ……………(ii)
∴ ∠ FOE = 30° , ∠ COB = 30° and ∠ DOE = 30° .