If A is facing east then he turn 100° in the clockwise direction and then again turn 145° in the anti-clockwise direction. Which direction A is facing now ?

Question

Accepted Answer

To determine the direction A is facing after the given turns, we need to follow the sequence of rotations starting from the initial direction.

1. **Initial Direction**: A is initially facing East.

2. **First Turn**: A turns 100° clockwise.
   - Starting from East, a 90° clockwise turn would point A towards South. Since A turns 100°, which is 10° more than 90°, A will be facing 10° past South towards the West. This direction is South-South-West.

3. **Second Turn**: A turns 145° anti-clockwise.
   - From South-South-West, turning 145° anti-clockwise means moving back towards the East. A 90° anti-clockwise turn from South-South-West would point A towards East, and an additional 55° (145° - 90°) would point A towards North-East.

Therefore, after both turns, A is facing North-East.

**Explanation of Options**:

1. **North**: This option is incorrect because after the turns, A does not align with the North direction. The calculations show that A ends up facing North-East, not directly North.

2. **East**: This option is incorrect because although A starts facing East, the subsequent turns change his direction. After the turns, A ends up facing North-East, not East.

3. **South-West**: This option is incorrect because after the first turn, A is near South-South-West, but the second turn moves him away from this direction. The final direction is North-East, not South-West.

4. **North-East**: This is the correct option. After the sequence of turns, A ends up facing North-East, as explained in the detailed breakdown above.

Thus, the correct answer is Option 4: North-East.