Two lines AB and CD intersect at O. If ∠AOC +∠COB+∠BOD = 270°, find the measures of ∠AOC, ∠COB, ∠BOD and ∠DOA.

∠AOC + ∠COB + ∠BOP = 270^o

To find: ∠AOC, ∠COB, ∠BOD and ∠BOA

Here, ∠AOC + ∠COB + ∠BOD + ∠AOD = 360^o(Complete angle)

270^o + ∠AOD = 360^o

∠AOD = 360^o – 270^o

= 90^o

Now,

∠AOD + ∠BOD = 180^o(Linear pair)

90^o + ∠BOD = 180^o

Therefore,

∠BOD = 90^o

∠AOD = ∠BOC = 90^o(Vertically opposite angle)

∠BOD = ∠AOC = 90^o(Vertically opposite angle)