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In figure, BO and CO are the bisectors of exterior angles $∠ B$ and $∠ C$ of $Δ A B C .$ Find $∠ B O C .$

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50 °

60 °

40 °

30 °

answer is A.

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Detailed Solution

Given is a figure,
Question Image

BO and CO are the bisectors of

∠ B

and

∠ C

respectively.
ABC and BOC are triangles.
BO is the bisector of

∠ B

∠ B = 2 ∠ C B O

∠ A B C + 2 ∠ C B O = 180 °

[linear pair]

⇒ 2 ∠ C B O = 180 ° − 50 °

⇒ ∠ C B O = 65 °

CO is the bisector of

∠ C

∠ C = 2 ∠

BCO

∠ A C B + 2 ∠ B C O = 180 °

[linear pair]

⇒ 2 ∠ B C O = 180 ° − 60 °

⇒ ∠ B C O = 60 °

Δ B O C

∠ B O C + ∠ B C O + ∠ C B O = 180 °

(Angle sum property of a triangle)

∠ B O C = 180 ° − 60 ° − 70 °

⇒ ∠ B O C = 50 °

Thus, the value of

∠ B O C = 50 °

.
Therefore, option (1) is correct.

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