In the figure BO and CO are bisectors of Angle B and angle C respectively. find the value of angle BOC where angle A is 50°.
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In the figure BO and CO are bisectors of Angle B and angle C respectively. find the value of angle BOC where angle A is 50°.
Please tell me fast
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Answer:
As BO and CO are the angle bisectors of external angles of△ABC, Then
∠1=∠2
∠4=∠3
We know, ∠A+∠ABC+∠ACB=180 ∘. …eqn(1)
And ∠ABC=180−2∠1
∠ACB=180−2∠4
Putting it in the eqn (1), we get
∠A+180−2∠1+180−2∠4=180
⇒∠1+∠4=90+ 1/2 ×∠A. …eqn(2)
Also we know from the figure, ∠BOC+∠1+∠4=180 ∘
∠BOC=180−∠1−∠4
From eqn (2)
∠BOC=180−90− 1/2× ∠A
⇒∠BOC=90 ∘ − 1/2× ∠A
=90 - 1/2 × 50
ANS =65°
Answer:
sorry the given question is confusing