Making a shelf

[quakerboy]

9. Try it with a piece of paper.

I guarantee you are wrong on this. If you cut a straight board at a 45 degree angle, you end up with 2 boards that each have a 45 degree angle on the pointy end and 135 on the obtuse corner. Flip one side, put the cut ends together, acute corner to acute corner, obtuse to obtuse, you get a 90 degree angle inside.

If you cut it at 30 degree angle, you get two pieces that have 30 degree angles on the point and 150 on the obtuse corner. Putting that together, you end up with only a 60 degree interior angle.

I will agree with you that it is hard to explain without illustrations. Try it with 3 strips of paper if you don't believe me. Cut across one at 45, one sharper, and one flatter. Then flip them, you will get one right corner, one that is more obtuse, and one that is more acute.