MathematicsIn figure, O is center of circle and ∠PQR=1150. Then, which of the following is the measure of ∠POR (inscribed)?

In figure, O is center of circle and ∠PQR=1150. Then, which of the following is the measure of ∠POR (inscribed)?


  1. A
    1300
  2. B
    2300
  3. C
    2700
  4. D
    3600  

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    Solution:

    Consider the given figure,
    Here,
    ∠PQR=1150.
    Major angle,
    ∠POR=2∠PQR  x=2×115o  x=2300 Sum of angles formed at center of circle is 3600. ∴∠POR+x=3600 ⇒∠POR+2300=3600 ⇒∠POR=3600–2300 ⇒∠POR=1300 Hence, the measure of ∠POR is 1300.
    Therefore, option 1 is correct.
     
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