A man is initially facing East.\nHe turns 60 degrees in the anticlockwise (left) direction and then again turns another 120 degrees in the same anticlockwise direction.\nAfter completing these two turns, in which direction is he finally facing?

Introduction / Context:
This is a pure turning and orientation problem without any distances. A man starts facing East and takes two anticlockwise turns: one of 60 degrees and another of 120 degrees. We must find his final facing direction. Such questions test understanding of angles on a compass, the meaning of anticlockwise rotation, and the fact that the net effect of multiple rotations is the sum of the angles in the same direction.

Given Data / Assumptions:

• The man initially faces East.
• He turns 60 degrees in the anticlockwise (left) direction.
• Then he turns another 120 degrees in the same anticlockwise direction.
• We must determine his final facing direction after both turns.
• We assume a full circle is 360 degrees and directions are spaced at 90 degree intervals (East, North, West, South, back to East).

Concept / Approach:
When a person turns through multiple angles in the same rotational direction, the total rotation is just the sum of the angles. Here, both rotations are anticlockwise, so we add 60 degrees and 120 degrees to get 180 degrees of anticlockwise rotation. Starting from East, an anticlockwise rotation of 90 degrees leads to North, and a further 90 degrees (total 180 degrees) leads to West. Therefore, his final direction is West. We do not need to worry about intermediate diagonal directions because the net rotation is exactly 180 degrees, corresponding to one of the main cardinal directions.

Step-by-Step Solution:
Step 1: Start by marking East as the initial direction. Step 2: The man first turns 60 degrees anticlockwise from East. This places him somewhere between East and North, closer to East, but we do not need to label this intermediate direction precisely yet. Step 3: He then turns another 120 degrees anticlockwise from his current orientation. Step 4: The total anticlockwise rotation is 60 + 120 = 180 degrees from his original facing direction (East). Step 5: On a compass, a 90 degree anticlockwise rotation from East leads to North, and another 90 degrees (making 180 degrees total) leads to West. Step 6: Therefore, after the two turns, he ends up facing West.

Verification / Alternative check:
We can also think in terms of cardinal points as angle measures: East can be treated as 0 degrees, North as 90 degrees, West as 180 degrees and South as 270 degrees, all measured anticlockwise. Starting at East (0 degrees), a 180 degree anticlockwise rotation brings him to angle 180 degrees, which is West. Since the net rotation is exactly 180 degrees, there is no need to consider fractional or diagonal directions such as North-East or South-East. This confirms that West is the correct final direction.

Why Other Options Are Wrong:
East would require either no rotation or a multiple of full 360 degree turns, which we do not have here. North-West would correspond to a 135 degree anticlockwise rotation from East, not 180 degrees. South-East is 315 degrees anticlockwise from East (or 135 degrees clockwise), which does not match the given rotations. North is only 90 degrees anticlockwise from East, which occurs halfway through his full rotation, not at the end. Thus, West is the only direction consistent with a total of 180 degrees anticlockwise rotation from East.

Common Pitfalls:
A common mistake is to add angles incorrectly or to forget that both turns are in the same anticlockwise direction, leading to subtraction instead of addition. Some learners also misplace the directions on the circle, mixing up the order of North, West and South. Drawing a simple circle with East on the right, North at the top, West on the left and South at the bottom, and then marking the 180 degree anticlockwise rotation, is an excellent way to visualize the correct final direction quickly.

Final Answer:
After the two anticlockwise turns, the man is finally facing towards the West.