MathematicsIn Fig. if ∠ABC = 20º, then ∠AOC is equal to ____.

In Fig. if ABC = 20º, then AOC is equal to ____.


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    Solution:

    In Fig. if ABC = 20º, then AOC is equal to 40 °  .
    Given that, ABC= 20 °  .
    From figure we can see that, the angle made by an arc at the center is AOC  , and the angle made by arc at the circumference is ABC= 20 °  .
    Since the angle made by an arc at the center is two times the angle made by it at any point on the remaining part of the circle, so AOC=2×ABC  .
      AOC=2× 20 °   AOC= 40 °   Therefore, required angle is 40 °  .
     
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