Enigma 1532: Just reflecting
From New Scientist #2695, 14th February 2009 [link]
Joe has been showing Penny a few optical experiments. In one experiment he placed six mirrors vertically to form a regular hexagon with small gaps between the mirrors. Through one gap he shone a laser beam so it emerged straight from the gap diametrically opposite.
Penny then had to work out the smallest angle through which the beam must be rotated so that it emerged from the same gap as before, after being reflected just once by all six mirrors.
What was that small angle (rounded to the nearest degree)?