Anil is facing the east direction. He then turns 90 degrees clockwise and then turns 135 degrees anti clockwise. After making these two turns, in which direction is he now facing?

Introduction / Context:
This is a straightforward orientation question. Anil initially faces east, then rotates through a right angle clockwise and then through 135 degrees anti clockwise. The task is to find his final facing direction. It tests basic understanding of clockwise and anti clockwise rotations and the layout of the four main directions plus diagonals on a circle.

Given Data / Assumptions:

• Anil starts facing east.
• He turns 90 degrees clockwise.
• He then turns 135 degrees anti clockwise.
• We use a standard compass where north is at 0 degrees, east at 90 degrees, south at 180 degrees, west at 270 degrees, and north east at 45 degrees.

Concept / Approach:
We can represent directions as angles and treat rotations as additions or subtractions of these angles. Clockwise rotation is taken as increasing the angle from the reference, while anti clockwise rotation is taken as decreasing it, or vice versa, as long as we are consistent. The key is to compute the net angular position after both rotations relative to north and then interpret that angle as a known direction such as north east or west.

Step-by-Step Solution:
Step 1: Represent east as 90 degrees.Step 2: A 90 degree clockwise turn from east leads to south, which corresponds to 180 degrees.Step 3: From south at 180 degrees, Anil now turns 135 degrees anti clockwise. Subtracting 135 degrees gives 180 − 135 = 45 degrees.Step 4: An angle of 45 degrees is exactly halfway between north (0 degrees) and east (90 degrees), which corresponds to the north east direction.Step 5: Therefore, after both rotations, Anil is facing north east.

Verification / Alternative check:
We can also reason by directions alone. From east, a 90 degree clockwise turn leads to south. From south, a 90 degree anti clockwise turn leads back to east, and another 45 degrees anti clockwise moves him further towards north, landing at north east. This stepwise reasoning, broken into a 90 degree and a 45 degree anti clockwise component, confirms the angle calculation and supports the conclusion that Anil faces north east at the end.

Why Other Options Are Wrong:
North would require a total rotation that brings him exactly opposite south, which is not achieved with a 90 clockwise and a 135 anti clockwise turn. West lies opposite east and would involve a 270 degree shift, which does not match the net change here. South west is between south and west, but Anil ends between north and east instead. South east is not possible because he moves away from the southern region in his final anti clockwise rotation. Only north east fits both the numerical angle and the intuitive compass reasoning.

Common Pitfalls:
Common errors include forgetting to change the sign of the second rotation and adding 90 and 135 in the same direction, or misreading clockwise and anti clockwise. Some learners incorrectly assume that a larger second rotation always dominates without checking the final angle. Using a simple angle representation or drawing the directions as points on a circle and moving step by step around it helps avoid these mistakes.

Final Answer:
After turning 90 degrees clockwise and then 135 degrees anti clockwise from facing east, Anil is finally facing towards the North-East.