Two lines AB and CD intersect at O. If ∠AOC +∠COB+∠BOD = 270°,

1.	Two lines AB and CD intersect at O. If ∠AOC +∠COB+∠BOD = 270°, find the measures of ∠AOC, ∠COB, ∠BOD and ∠DOA.
Answer» ∠AOC + ∠COB + ∠BOP = 270° To find: ∠AOC, ∠COB, ∠BOD and ∠BOA Here, ∠AOC + ∠COB + ∠BOD + ∠AOD = 360°(Complete angle) 270° + ∠AOD = 360° ∠AOD = 360° – 270° = 90° Now, ∠AOD + ∠BOD = 180°(Linear pair) 90° + ∠BOD = 180° Therefore, ∠BOD = 90° ∠AOD = ∠BOC = 90°(Vertically opposite angle) ∠BOD = ∠AOC = 90°(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.

Answer»

∠AOC + ∠COB + ∠BOP = 270°

To find:

∠AOC, ∠COB, ∠BOD and ∠BOA

Here,

∠AOC + ∠COB + ∠BOD + ∠AOD = 360°(Complete angle)

270° + ∠AOD = 360°

∠AOD = 360° – 270°

= 90°

Now,

∠AOD + ∠BOD = 180°(Linear pair)

90° + ∠BOD = 180°

Therefore,

∠BOD = 90°

∠AOD = ∠BOC = 90°(Vertically opposite angle)

∠BOD = ∠AOC = 90°(Vertically opposite angle)