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

Question

Two lines AB and CD intersect at O . If &#x2220; AOC + &#x2220; COB + &#x2220; BOD = 270&#xB0;, find the measures of &#x2220; AOC , &#x2220; COB , &#x2220; BOD and &#x2220; DOA .

Philoid · Accepted Answer

∠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)

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