Updated

The angle question seems to be solved. Well done to both Rick and Ben.

The square root of 2 thing, is actually quite easy for anybody interested, you begin by saying let root(2)= m/n where m,n are integers, n non-zero. Without loss of generality you can assume they have no common divisors because you could just divide them out and then start from there. You then find that 2 is a common divisor, thus there is a contradiction so the inition assumption that such an m and n exist is false. It's quite neat.

Have a good solid think at the other one. Its really quite amazing that it is possible I reckon.