Meet starts cycling early in the morning, facing the Sun. After some time, he takes a `45^(@)` turn to his left and then again 7 turns `80^(@)` towards his left. In which direction is be now with respect to his initial position?

Options

A. South-East
B. South-West
C. North-West
D. Notth-East

Answer

To solve the problem step by step, we will analyze the turns made by Meet and calculate his final direction with respect to his initial position.

### Step 1: Initial Direction
Meet starts cycling early in the morning, facing the Sun. In the morning, the Sun rises in the East. Therefore, his initial direction is East.

### Step 2: First Turn
Meet takes a 45-degree turn to his left.
- When facing East, a left turn of 45 degrees will point him towards the North-East direction.

### Step 3: Second Turn
Next, Meet takes 7 turns of 80 degrees each towards his left.
- The total angle turned in this step is calculated as:
\[ \text{Total turn} = 7 \times 80^\circ = 560^\circ \]

### Step 4: Total Angle Calculation
Now, we need to add the first turn (45 degrees) to the total turn from the second step:
\[ \text{Total angle turned} = 560^\circ + 45^\circ = 605^\circ \]

### Step 5: Reducing the Angle
Since a full circle is 360 degrees, we can reduce the total angle to find the effective turn:
\[ \text{Effective turn} = 605^\circ - 360^\circ = 245^\circ \]

### Step 6: Determining Final Direction
Now, we need to determine the direction corresponding to a 245-degree turn from the initial East direction:
- 0 degrees is East.
- 90 degrees is North.
- 180 degrees is West.
- 270 degrees is South.

To find 245 degrees:
- 245 degrees is between 180 degrees (West) and 270 degrees (South).
- Specifically, it is 65 degrees past 180 degrees (West).

Thus, the final direction is South-West.

### Conclusion
Meet is now facing South-West with respect to his initial position.

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