P started from his house walking towards the West. After walking 25 m, he turned right and walked 10 m, then turned right again and walked 15 m. After this, he has to turn right through an angle of 135 degrees and walk 30 m. In which direction should he go on this last leg?

Introduction:
This question combines straightforward direction movements with a slightly unusual turn of 135 degrees. P moves West initially, then makes two right-angle turns, and finally is asked to turn right through 135 degrees before walking further. We must determine the resulting direction of travel for this last segment.

Given Data / Assumptions:
• P starts from his house walking towards the West.• He walks 25 m, turns right and walks 10 m.• He turns right again and walks 15 m.• After that, he is to turn right through 135 degrees and walk 30 m.• We are asked only for the direction of this last leg, not his exact coordinates.

Concept / Approach:
The critical part is to track P's current facing direction before the 135 degree turn. Right and left turns are taken relative to the person's current direction. After determining that direction, we then imagine a 135 degree right turn, which corresponds to three 45 degree steps or one and a half right angles. On the compass, moving 135 degrees right from a given cardinal direction will land us on one of the diagonal directions (like South-West or South-East).

Step-by-Step Solution:
Step 1: Initially, P faces West and walks 25 m. His facing direction remains West.Step 2: He turns right from West. On a compass, right from West points North. He walks 10 m North and is now facing North.Step 3: He then turns right again from North, which points East. He walks 15 m East and is now facing East.Step 4: Now he must make a right turn of 135 degrees from East. A 90 degree right turn from East would take him to South. An additional 45 degrees right from South leads to South-West.Step 5: Therefore, a single 135 degree right turn from East results in the direction South-West.Step 6: Thus, on his last leg, P should go in the South-West direction.

Verification / Alternative check:
Think of the circle of directions: East → South-East (45 degrees) → South (90 degrees) → South-West (135 degrees) → West (180 degrees). Starting from East and turning right (clockwise) by 135 degrees takes you three steps to South-West. This matches our earlier breakdown of a 90 degree plus an additional 45 degree right turn.

Why Other Options Are Wrong:
West would correspond to a 180 degree right turn from East, which is not what is specified. South would correspond to only a 90 degree right turn. South-East would result from only a 45 degree right turn. North-West is on the opposite diagonal and would require a different rotation (for example, 135 degrees left from East, not right). Only South-West matches exactly a 135 degree right turn from East.

Common Pitfalls:
Many students misread "right at 135 degrees" as "right, then 135 degrees more", or confuse 135 degrees with 45 degrees. Some also forget to update P's facing direction after the earlier two right turns and assume he is still facing West. A good method is to draw a small compass, mark the current facing direction, and count 45 degree steps in the correct direction to reach the final orientation.

Final Answer:
On the last leg, after turning right through 135 degrees, P should walk towards the South-West direction.