I am facing West. I turn $$100^\circ$$ in the anticlockwise direction and then $$145^\circ$$ in the clockwise direction. Which direction am I facing now?

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Accepted Answer

1. **Initial Direction**: Facing West.  
2. **Anticlockwise Turn**: Turning $$100^\circ$$ anticlockwise from West moves towards South-West and slightly beyond.  
3. **Clockwise Turn**: From this position, turning $$145^\circ$$ clockwise effectively results in a net clockwise movement of:  
   $$
   145^\circ - 100^\circ = 45^\circ.
   $$
   This places the person at **North-West**.

Thus, the correct answer is **(b) North-West**.

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