Question : AB is the diameter of a circle with centre O. P is a point on it. If $\angle$POA = 120°. Then $\angle$PBO = ?
Option 1: 60°
Option 2: 120°
Option 3: 45°
Option 4: 50°
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Correct Answer: 60°
Solution :
$\angle$AOB = 180°
$\angle$AOP = 120°
we know that , $\angle$AOP + $\angle$POB = 180°
∴ $\angle$POB = 180° – 120° = 60°
OP = OB = radius
∴ $\angle$OPB = $\angle$PBO = $\frac{120°}{2}=60°$ ($\because $ OP = OB)
Hence, the correct answer is 60°.
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