Question

Please help me solve this

answer is 70

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Answer 1

70°

Explanation:

• 
  `In\:\triangle ABC,\:\measuredangle A =40\degree` (Given)

• 
  `Let \:\measuredangle ABC= x \: and \:\measuredangle ACB = y`

• 
  `40\degree + x + y = 180\degree` (sum of the angles of a triangle)

• 
  `\rightarrow x + y = 180\degree-40\degree`

• 
  `\rightarrow\bold{\red{ x + y = 140\degree}}`....(1)

• 
  `\measuredangle CBD + x = 180\degree` (angles in linear pair)

• 
  `\rightarrow x = 180\degree-\measuredangle CBD`....(2)

• 
  `\measuredangle BCE + y = 180\degree` (angles in linear pair)

• 
  `\rightarrow y = 180\degree-\measuredangle BCE`....(3)

• 
  `\rightarrow x+y = 180\degree-\measuredangle CBD+180\degree-\measuredangle BCE` (Adding equations 2 and 3)

• 
  `\rightarrow 140\degree= 360\degree-(\measuredangle CBD+\measuredangle BCE)`

• 
  `\rightarrow\measuredangle CBD+\measuredangle BCE= 360\degree- 140\degree`

• 
  `\rightarrow\measuredangle CBD+\measuredangle BCE= 220\degree`

• 
  `\rightarrow(1)/(2)(\measuredangle CBD+\measuredangle BCE)= (1)/(2)*220\degree` (Dividing throughout by 2)

• 
  `\rightarrow(1)/(2)\measuredangle CBD+(1)/(2)\measuredangle BCE= 110\degree`

• 
  `\rightarrow \measuredangle CBO+\measuredangle BCO= 110\degree`....(4) (BO and CO are bisectors of angle CBD and angle BCE respectively)

• 
  `In\:\triangle OBC`

• 
  `\measuredangle CBO+\measuredangle BCO+\measuredangle BOC= 180\degree` (Sum of the angles of a triangle)

• 
  `\rightarrow 110\degree+\measuredangle BOC= 180\degree` (From equation 4)

• 
  `\rightarrow \measuredangle BOC= 180\degree-110\degree`

• 
  `\rightarrow \huge{\orange{\measuredangle BOC= 70\degree}}`