Meet starts cycling early in the morning while facing the Sun, so he is initially facing east. After some time, he takes a 45 degree turn to his left. Then he again turns 80 degrees towards his left. In which direction is he now with respect to his initial position?

Introduction / Context:
This question combines knowledge of the Sun's direction in the morning with angular turns measured in degrees. It tests whether candidates can track cumulative rotations from an initial facing direction. Meet starts by facing east, then makes two left turns of 45 degrees and 80 degrees respectively. The challenge is to identify the final compass direction he faces after adding these rotations.

Given Data / Assumptions:

• Early in the morning, the Sun appears in the east, so Meet initially faces east.
• He first turns 45 degrees to his left from the east direction.
• He then makes another turn of 80 degrees to his left.
• We assume all degree measures are exact and measured in the usual geometric sense.
• We need the final compass direction that he faces after these two left turns.

Concept / Approach:
Facing east corresponds to a direction 90 degrees clockwise from north if we use the usual bearing convention, but for this problem it is simpler to think in terms of the four quadrants. East is to the right, north is up, west is left and south is down. A left turn from east takes us towards north. By adding the angles of the two left turns, we find the total anticlockwise rotation from east and then determine which quadrant that final direction falls into.

Step-by-Step Solution:
Step 1: Meet is initially facing east. Step 2: A left turn is an anticlockwise rotation. From east, turning 90 degrees left would make him face north. However, he turns only 45 degrees left, so he faces exactly halfway between east and north, which is the north east direction. Step 3: From the north east direction, he turns another 80 degrees to his left. Step 4: The total leftward rotation from the original east direction is 45 degrees plus 80 degrees, which equals 125 degrees. Step 5: Now map this total rotation. From east, rotating 90 degrees left brings him to north. An additional 35 degrees left (since 125 minus 90 equals 35) moves him beyond north towards the west. Step 6: Therefore, after a total rotation of 125 degrees, he is in the quadrant between north and west, closer to west than north but still above the horizontal axis, which is the north west direction.

Verification / Alternative check:
An angular bearing view can also be used. Let east be 0 degrees, north be 90 degrees, west be 180 degrees and south be 270 degrees. A left turn from east increases the angle. After 125 degrees anticlockwise rotation from east, the bearing is 125 degrees from east, which corresponds to 90 plus 35 degrees from north, hence lying between north (90) and west (180). Since 125 degrees is less than 180 degrees, the direction is in the north west quadrant, which confirms the earlier reasoning.

Why Other Options Are Wrong:

• Option A, South-East, would be in the opposite quadrant, requiring a rotation towards the south rather than north.
• Option B, South-West, is too far anticlockwise, corresponding to rotations greater than 180 degrees.
• Option D, North-East, would be correct if the second left turn were small or zero; however the additional 80 degrees pushes him beyond north.
• Option E, West, would require a total rotation of exactly 180 degrees from east, not the given 125 degrees.

Common Pitfalls:
Many students treat the two left turns as independent and forget to combine them, or they misinterpret 45 degrees plus 80 degrees as a full right angle. Others incorrectly believe that any series of left turns from east will always lead exactly to north or west. Accurately adding the degree measures for rotations and then mapping them on a simple compass-like circle is a reliable way to avoid such mistakes.

Final Answer:
After turning 45 degrees and then 80 degrees to his left from the east, Meet is facing towards the North-West direction.