MathematicsIn given figure, ∠OAB = 30º and ∠OCB = 57º. What measure of ∠AOC.

In given figure, ∠OAB = 30º and ∠OCB = 57º. What measure of ∠AOC.


Chart Description automatically generated

  1. A
    120 °  
  2. B
    160 °  
  3. C
    180 °  
  4. D
    240 °   

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    Solution:

    Given that,  .
    Chart Description automatically generatedConsidering the triangle OAB,  
    Radius of the circle is OA=OB.  
    Also, we know that the angles opposite to the equal sides are equal.
    So, ∠OBA=∠BAO= 30 °  .
    Considering triangle AOB,   The sum of angles in a triangle is 180 °   .
      ∠AOB+∠OBA+∠BAO= 180 °   ∠AOB+ 30 ° + 30 ° = 180 °   ∠AOB+ 60 ° = 180 °   ∠AOB= 180 ° − 60 °   Hence option 1 is correct.
     
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