in the given figure BO and CO are the bisectors of the exterior angles meeting each other at O. if angle a =7 0 degrees find angle BOC
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This is the direct formula for finding this type of questions .
If you want to proof of this formula I can give you.
If you want to proof of this formula I can give you.
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adityaadi1:
haa please give md
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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
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