In Fig. 6.13, lines AB and CD intersect at O. If ∠ AOC + ∠ BOE = 70° and ∠ BOD = 40°, find ∠BOE and reflex ∠COE.

From Fig. 6.13,

∠AOC + ∠BOE +∠COE and ∠COE +∠BOD + ∠BOE form a straight line.

So, ∠AOC + ∠BOE +∠COE = ∠COE +∠BOD + ∠BOE = 180^o

Now, by putting the values of ∠AOC + ∠BOE = 70^o and ∠BOD = 40^o we get,

70^o +∠COE = 180^o

∠COE = 110^o and

∠BOE = 30^o