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      Question

      MN is a diameter of a circle with centre O. The tangent

      at 'P' meets MN produced at 'Q'. If ∠PMN = 44 ° , then find ∠PNQ.
      A 134° Correct Answer Incorrect Answer
      B 124° Correct Answer Incorrect Answer
      C 104° Correct Answer Incorrect Answer
      D 144° Correct Answer Incorrect Answer

      Solution

      Image
      Angle made by the diameter of a circle on the arc of the circle is 90 o  i.e. ∠MPN = 90 ° .

      Sum of each angle in a triangle is 180 o .

      So, ∠PMN + ∠PNM + ∠MPN = 180 °

      Or, 44 °  + ∠PNM + 90 °  = 180 °

      Or, ∠PNM = 180 °  - 134 °

      Or, ∠PNM = 46 °

      Now, ∠PNM + ∠PNQ = 180 o  (Linear pair of angles)

      So, ∠PNQ = 180 - 46 = 134 °

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