Starting from a point, a person travels 3 km towards the East and then turns left to travel 4 km towards the North.\nAfter that he again turns to his left by 45° and continues to walk straight.\nIn which direction is he now facing after this final turn?

Introduction / Context:
This question tests understanding of both right-angle and non-right-angle turns in direction sense. The person first moves along two perpendicular directions (East then North) and then makes a further 45 degree left turn from his current facing direction. We are not asked to find his position, but specifically to determine the direction he is facing after the last turn. Correctly interpreting left turns and angles is crucial here.

Given Data / Assumptions:

• The person starts from an initial point.
• He travels 3 km towards the East.
• He then turns left and travels 4 km, which implies moving towards the North.
• After that, he again turns to his left by 45 degrees.
• We must find the direction he is facing after this 45 degree left turn.
• We assume standard compass directions and that 45 degree turns lie halfway between two main cardinal directions.

Concept / Approach:
The key is to track the orientation of the person, not his exact position. Initially, he faces East. A left turn from East gives North. Another left turn of 90 degrees from North would give West, but here he turns only 45 degrees to the left, which means he ends up facing exactly halfway between North and West, that is, North-West. Remember that turning left means rotating anticlockwise on the compass, and a 45 degree turn corresponds to moving to a diagonal direction between two main directions.

Step-by-Step Solution:
Step 1: At the start, the person begins by walking 3 km towards the East. Therefore, his initial facing direction is East. Step 2: From facing East, he makes a left turn. A 90 degree left turn from East points towards North. He then walks 4 km North, so his current facing direction is North. Step 3: Now, from facing North, he again turns to his left, but this time the turn is 45 degrees, not a full 90 degrees. Step 4: Visualize the compass: to the left (anticlockwise) of North is West. The direction exactly halfway between North and West is North-West, which is at a 45 degree angle between them. Step 5: Because he rotated 45 degrees anticlockwise from North, his new facing direction is therefore North-West.

Verification / Alternative check:
A simple compass diagram can verify this. Mark East, North and West on a circle. From East to North is a 90 degree anticlockwise turn, which matches the first left turn. From North, another full 90 degree left turn would reach West, but this problem specifies only a 45 degree left turn, so his direction lies exactly halfway between North and West. That intermediate direction is labelled North-West on the standard eight-direction compass, confirming our reasoning without any coordinate calculations.

Why Other Options Are Wrong:
North-East is to the right of North (clockwise) and would result from a right turn, not a left one. South-East and South-West are below the East–West line and would require turning around past the South direction, which is not mentioned here. East would correspond to his initial facing direction, which he has clearly changed twice by turning left. Thus, only North-West matches a 45 degree left turn from a North-facing orientation.

Common Pitfalls:
A common error is to treat the 45 degree left turn as if it were another 90 degree left turn, which would lead to West instead of North-West. Another mistake is confusing clockwise and anticlockwise rotations when interpreting left and right. To avoid these pitfalls, always imagine yourself facing the given direction and then mentally rotate in the specified sense by the required angle, or quickly sketch a compass with the angles marked at 45 degree intervals.

Final Answer:
After turning left by 45 degrees from North, the person is facing towards the North-West direction.