In projective geometry the dual of the cross ratio dual is an angle measurement? I am trying to get my head around angles in projective geometry.
I understand (more or less) the cross ratio and that it can be seen as an distance measurement. (for example in the Beltrami Cayley Klein model of hyperbolic geometry)
But then there is its dual where the cross ratio is some kind of angle measurement of lines?
I just draw a blank here 
which lines are mend here? can anybody give some light?

You can define angles in terms of the cross ratio (of lines) and the circular points at infinity.
If you have two lines that intersect at the point P, you can draw two more lines from P to the circular points at infinity. Taking the natural logarithm of this will give you the Euclidean angle between the two original lines times i (up to multiples of 2πi depending on branch).
The circular points at infinity add just enough structure to projective geometry to let you tell circles apart from other conics, this turns out to give enough structure to define angles.
The same construction can be used to define hyperbolic angles, a.k.a. rapidity. In that case, instead of drawing lines to the circular points at infinity, you pick a pair of real points that define asymptotes for a unit hyperboloid in Minkowski space. This gives the relation between the distances using cross ratios in the Beltrami-Klein model and hyperbolic angles in the hyperboloid model.
