A girl is initially facing north. She first rotates through an angle of 100 degrees in the clockwise direction and then rotates through 190 degrees in the anticlockwise direction. After performing both these rotations, in which cardinal direction is the girl finally facing?

Introduction / Context:
This direction sense problem focuses on rotation through given angles and asks for the final facing direction. The starting direction is north, and the girl rotates clockwise and then anticlockwise through specific angles. Such questions test the understanding of clockwise versus anticlockwise rotation and how to combine angle measures to find a net change in direction.

Given Data / Assumptions:

• The girl starts by facing north.
• She rotates 100 degrees clockwise.
• Then she rotates 190 degrees anticlockwise.
• We consider a full circle as 360 degrees with north, east, south, and west at right angle intervals.
• Clockwise rotation is taken as a negative change and anticlockwise as a positive change when combining angles.

Concept / Approach:
The key idea is to calculate the net rotation. Instead of tracking every intermediate orientation in detail, we can treat clockwise rotation as negative and anticlockwise as positive and simply add the angles. The resulting net angle tells us how far from the initial direction the person has turned. Once we know the net angle relative to north, we map that angle to a cardinal direction such as east, south, west, or an intermediate direction.

Step-by-Step Solution:
Step 1: Start with the initial direction as north.Step 2: The first rotation is 100 degrees clockwise, which we treat as −100 degrees.Step 3: The second rotation is 190 degrees anticlockwise, which we treat as +190 degrees.Step 4: Add the rotations to get the net change in direction: −100 + 190 = +90 degrees.Step 5: A net change of +90 degrees anticlockwise from north means we rotate from north through west, because 90 degrees anticlockwise from north lands at west.Step 6: Therefore, after both rotations, the girl is facing west.

Verification / Alternative check:
We can also track intermediate directions more explicitly. Starting facing north, a 100 degree clockwise turn moves her 90 degrees to east and then 10 degrees further, so she ends up slightly south of east. From there, turning 190 degrees anticlockwise carries her through north (100 degrees), then to west (190 degrees total), which leaves her exactly facing west. This stepwise reasoning matches the net angle method and confirms that west is the correct final direction.

Why Other Options Are Wrong:
North east and south east would correspond to net rotations of 45 or 315 degrees, which do not match the calculated net 90 degree change. South would correspond to a 180 degree shift from north and also does not fit the 90 degree net rotation. North west requires a 270 degree anticlockwise rotation, which again is inconsistent with the computed net change. Only west aligns with a net 90 degree anticlockwise rotation from the initial north facing position.

Common Pitfalls:
Learners sometimes incorrectly add both angles as if they were in the same direction, giving 290 degrees, and then try to map that directly to a direction. Another mistake is to confuse clockwise with anticlockwise and subtract in the wrong order. It is safer to assign signs to the rotations and then add them algebraically, or to draw a simple diagram with the four main directions and track each rotation step by step.

Final Answer:
After rotating 100 degrees clockwise and then 190 degrees anticlockwise, the girl ends up facing towards the West.