Random Stuff➝The Triangle Problem

This is a deceptively simple looking problem, all you have to do is work out the angle α in the following diagram.

I'd suggest you give it a good go, if you can find the solution on your own then you should feel very proud. If you can't hack it any longer though you can find the solution, with three related ways to prove it, below.

Well, the angle α is actually 20°, but what is interesting is how you show it. Here are three solutions on some grubby bits of paper.

Note, all three of the these solutions make use of the following simple dissection of an equilateral triangle: