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.Solution
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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