In a

ΔABC
, If

∠A=

60
°

,∠B=

80
°

and the bisectors of

∠B
and

∠C
meet at O, then the measure of

∠BOC
is ____°.

Question

In a

ΔABC
  , If

∠A=
    
     60
    °
   
   ,∠B=
    
     80
    °

and the bisectors of

∠B
  and

∠C
  meet at O, then the measure of

∠BOC
   is ____°.

Accepted Answer

In a

ΔABC
  , If

∠A=
    
     60
    °
   
   ,∠B=
    
     80
    °

and the bisectors of

∠B
  and

∠C
  meet at O, then the measure of

∠BOC
   is 120°.Given a triangle ABC in which

∠A=
    
     60
    °
   
   ,∠B=
    
     80
    °

and the bisectors of

∠B
  and

∠C
  meet at O.Using angle sum property in triangle ABC,

∠A + ∠B + ∠C = 180°

⇒60° + ∠B + ∠C = 180°

⇒∠B + ∠C = 180° − 60°

⇒∠B + ∠C = 120°……
      1

Dividing by 2,

⇒
      1
      2
     
     ∠B +
      1
      2
     
     ∠C = 
      1
      2
     
     × 120°

⇒
      1
      2
     
      ∠B + 
      1
      2
     
     ∠C = 60°

⇒
      1
      2

∠B + ∠C 
      = 60°………….. 
      2

Using angle sum property in triangle BOC,

∠BOC + ∠OBC + ∠OCB = 180°

⇒∠BOC + 
      1
      2
     
     ∠B + 
      1
      2
     
     ∠C = 180°

⇒∠BOC + 
      1
      2
     
      
      
       ∠B + ∠C
      = 180°

⇒∠BOC + 60° = 180°

⇒∠BOC = 180° − 60°

⇒∠BOC = 120°

Hence, ∠BOC is 120°.Hence, the measure of

∠BOC
   is 120°.

In a $Δ A B C$ , If $∠ A = 60 °, ∠ B = 80 °$ and the bisectors of $∠ B$ and $∠ C$ meet at O, then the measure of $∠ B O C$ is ____°.

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In a ΔABC , If ∠A= 60 ° ,∠B= 80 ° and the bisectors of ∠B and ∠C meet at O, then the measure of ∠BOC is ____°.

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Detailed Solution

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In a $Δ A B C$ , If $∠ A = 60 °, ∠ B = 80 °$ and the bisectors of $∠ B$ and $∠ C$ meet at O, then the measure of $∠ B O C$ is ____°.