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In the figure given below, ABOP is a rectangle and O is the centre of the circle. It is also given that AB = BC and the measure of the angle ∠ABC is 60. Find the measure of the angle ∠OPN.
  • a)
    30
  • b)
    15
  • c)
    20
  • d)
    25
  • e)
    35
Correct answer is option 'B'. Can you explain this answer?
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In the figure given below, ABOP is a rectangle and O is the centre of ...
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In the figure given below, ABOP is a rectangle and O is the centre of ...
If ABC is 60 and AB=BC...then BAC=BCA=60Bcz of linear pair...BCA+BCN=180...hence...BCN=120Now...BCA+CBO=90...hence,CBO=30...Now, by angle sum property...CQB=30CQB=OQN(vertically opposite angles)Hence OQN=30Now,2PNQ=POQ(angle subtended at centre is twice the angle at arc)POQ=90Hence PNQ=45Now , in quadrilateral POQN...POQ+OQN+PQN+OPN=360(360-90)+30+45+OPN=360270+75+OPN=360OPN=360-345{OPN=15.}...
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