Meena faces East. She turns 135° in a counterclockwise direction and then 45° in the same direction and 225° in the clockwise direction. Which direction is she facing now?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → South-East
The eight directions are 45° apart, and North, East, South and West are 90° apart. Anticlockwise from East the order is North-East, North, North-West, West; clockwise from West it is North-West, North, North-East, East, South-East. Each turn is taken from the direction she is facing at that moment:
Facing East, 135° anticlockwise: 90° brings her to North and 45° more to North-West
Facing North-West, 45° more anticlockwise: West
Facing West, 225° clockwise: 90° to North, 180° to East and 45° more to South-East
Shortcut: Add up the turns and make one turn.
Anticlockwise: \(135^\circ+45^\circ=180^\circ\); clockwise: \(225^\circ\)
Net turn \(=225^\circ-180^\circ=45^\circ\) clockwise from East, which is South-East