Mathematics In given figure, ∠ACB = 40º. What is the value ∠OAB?

 In given figure, ∠ACB = 40º. What is the value ∠OAB?


  1. A
       50 °  
  2. B
       60 °  
  3. C
       40 °  
  4. D
       None of these 

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    Solution:

    Given that ∠ACB= 40 °  .
    Since we know the angle subtended by an arc at the center is two times the angle subtended by it at any point on the left part of the circle, so, ∠AOB=2∠ACB  .
    ⇒   ∠AOB=2 40 °   ⇒   ∠AOB= 80 °  
    Now, in  ΔAOB,   ⇒∠OAB=∠OBA   ⇒OA=OB  
    The sum of angles in a triangle is 180 °  .
     So, ∠OAB+∠OBA+∠AOB= 180 °  .
    ∠OAB+∠OAB+ 80 ° = 180 °  
      2∠OAB= 180 ° − 80 °   2∠OAB= 100 °   ∠OAB= 50 °   Hence, option 1 is correct.
     
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