This solution is from David Jeffreys

I think I have worked out the answer to getting an angle.

What you do is fold the paper in half (lengthways). Next you fold another so the crease touches a top corner (If you hold it as a landscape) and the corner below it touches the first crease.

The second layer at the bottom corner is 60 degrees. If you want to make it into an equilateral triangle you fold the over side so the fold has the other fold tucked right in and align it up with the other edge.

David supplied some diagrams like the one below.

The angles are 30 ^{o} and 60 ^{o} can be seen
if you consider an equilateral triangle of side 2a: