AB is the diameter of a circle with center O and P be a point on its circumference if $$\angle POA$$ = 120° then the value of $$\angle PBO$$ is 

Let $$\angle$$ PBO = $$\theta$$

$$\angle$$ AOP + $$\angle$$ POB = $$180^\circ$$     [Supplementary Angles]

=> $$120^\circ$$ + $$\angle$$ POB = $$180^\circ$$

=> $$\angle$$ POB = $$180^\circ-120^\circ=60^\circ$$

OB = OP = radius of circle

=> $$\angle$$ OBP = $$\angle$$ BPO = $$\theta$$

In $$\triangle$$ BOP,

=> $$\angle$$ POB + $$\angle$$ OBP + $$\angle$$ BPO = $$180^\circ$$

=> $$\theta + \theta + 60^\circ=180^\circ$$

=> $$2\theta=180^\circ-60^\circ=120^\circ$$

=> $$\theta=\frac{120^\circ}{2}=60^\circ$$

=> Ans - (B)