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A, O, B are three points on a line segment and C is a point not lying on AOB. If ∠AOC = 40° and OX, OY are the internal and external bisectors of ∠AOC respectively, then ∠BOY is    (SSC CGL 1st Sit. 2012)
  • a)
    70°
  • b)
    80°
  • c)
    72°
  • d)
    68°
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A, O, B are three points on a line segment and C is a point not lying ...

OX is the bisector of ∠AOC.
∴ ∠AOC = 2 ∠COX
OY is the bisector of ∠BOC.
∴ ∠BOC = 2 ∠COY
∴ ∠AOC + ∠BOC
= 2∠COY + 2∠COX = 180°
⇒ 2 (∠COX + ∠YOC) = 180°
⇒ ∠XOY = 90°
∴ ∠AOX + ∠XOY + ∠BOY = 180°
∴ ∠BOY = 180° – 90° – 20° = 70°
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Community Answer
A, O, B are three points on a line segment and C is a point not lying ...
We draw a line passing through C and intersecting the line segment AB at point D, then we can say that D is a point on the line segment AB.

In other words, D lies between A and B on the line segment AB.
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A, O, B are three points on a line segment and C is a point not lying on AOB. If ∠AOC = 40° and OX, OY are the internal and external bisectors of ∠AOC respectively, then ∠BOY is (SSC CGL 1st Sit. 2012)a)70°b)80°c)72°d)68°Correct answer is option 'A'. Can you explain this answer?
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