basic geometry knowledge.
Puzzle # 110ItalianoFrançais Prof. Gibbus' Angle
Prof. Gibbus find the angle a in the diagram below
(solve this puzzle using just basic geometry, no sines or cosines allowed!)
sent us this funny solution...
more seriously, the solution isn't as difficult as
it appears... You have just to change your point
of view (fig. 1)...
and look beyond the boundaries of the problem (fig.
2), as suggested in our tips
to puzzle solving. Actually, you can find the
solution without any calculation! Just extend the
grid and draw two lines as shown in the picture,
and you'll form a right isosceles triangle having
two opposite angles of 45
degrees. The base (or the hypothenuse) of the
triangle is parallel to the diagonal (the red line
in fig. 2) of the previous 1x3 rectangle. One leg
of the right triangle 'intersects' both parallels.
A transversal line which intersects a pair of parallel
lines produces pairs of alternate interior angles
which are EQUALS. So, angle a worths 45
winner of the puzzle of the month is: John
REIDY, Australia. Congratulations John!