A lighthouse beam points west. It rotates $45^\circ$ anticlockwise and then $270^\circ$ clockwise. In which direction does the beam point now?

Explanation

1. 01

   Net turn $= -45^\circ + 270^\circ = 225^\circ$ clockwise.

2. 02

   $225^\circ = 180^\circ + 45^\circ$: the opposite of west is east, and $45^\circ$ further clockwise is south-east.