text: # (solved)Question 10 SSC-CGL 2020 March 4 Shift 1
  
  In triangle ABC, ∠C = 68°, ∠B = 32°. The external angle bisectors of ∠B and ∠C meet at point O. Find ∠BOC.
  (Rev. 18-Jun-2024)
  
  ## Categories | About Hoven's Blog
  
  ,
  
  ### Question 10SSC-CGL 2020 Mar 4 Shift 1
  
  In triangle ABC, ∠C = 68°, ∠B = 32°. The external angle bisectors of ∠B and ∠C meet at point O. Find ∠BOC.
  
  ### Solution inBrief
  
  ∠A = 180 - (32 + 68) = 80. By a theorem in geometry, ∠BOC = 90 - (∠A/2). So ∠BOC = 90 - 80/2 = 50 degree answer!
  
  ### Solution in Detail
  
  BO is angle bisector, therefore,
  
  $\displaystyle \angle {OBC} = \frac{180 - 32}{2} = 74\degree$
  
  Similarly, we can deduce that
  
  $\displaystyle \angle {BCO} = \frac{180 - 68}{2} = 56\degree$
  
  From $\displaystyle \Delta OBC$ we get
  
  $\displaystyle x + 74 + 56 = 180$
  
  $\displaystyle \therefore x = 50 \degree\:\underline{Ans}$
  
  This Blog Post/Article "(solved)Question 10 SSC-CGL 2020 March 4 Shift 1" by Parveen is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
explanation: The document contains a math question from a SSC-CGL exam, along with a detailed solution and a brief explanation. The question asks for the measure of ∠BOC in a triangle ABC, given the measures of ∠B and ∠C, and the fact that the external angle bisectors of ∠B and ∠C meet at point O. The document also provides a step-by-step solution to the problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # (solved)Question 10 SSC-CGL 2020 March 4 Shift 1
  
  In triangle ABC, ∠C = 68°, ∠B = 32°. The external angle bisectors of ∠B and ∠C meet at point O. Find ∠BOC.
  (Rev. 18-Jun-2024)
  
  ## Categories | About Hoven's Blog
  
  ,
  
  ### Question 10SSC-CGL 2020 Mar 4 Shift 1
  
  In triangle ABC, ∠C = 68°, ∠B = 32°. The external angle bisectors of ∠B and ∠C meet at point O. Find ∠BOC.
  
  ### Solution inBrief
  
  ∠A = 180 - (32 + 68) = 80. By a theorem in geometry, ∠BOC = 90 - (∠A/2). So ∠BOC = 90 - 80/2 = 50 degree answer!
  
  ### Solution in Detail
  
  BO is angle bisector, therefore,
  
  $\displaystyle \angle {OBC} = \frac{180 - 32}{2} = 74\degree$
  
  Similarly, we can deduce that
  
  $\displaystyle \angle {BCO} = \frac{180 - 68}{2} = 56\degree$
  
  From $\displaystyle \Delta OBC$ we get
  
  $\displaystyle x + 74 + 56 = 180$
  
  $\displaystyle \therefore x = 50 \degree\:\underline{Ans}$
  
  This Blog Post/Article "(solved)Question 10 SSC-CGL 2020 March 4 Shift 1" by Parveen is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question from a SSC-CGL exam, along with a detailed solution and a brief explanation. The question asks for the measure of ∠BOC in a triangle ABC, given the measures of ∠B and ∠C, and the fact that the external angle bisectors of ∠B and ∠C meet at point O. The document also provides a step-by-step solution to the problem.
  
  Label: question-and-answer