In the rough sketch four concurrent lines are drawn in the Poincaré disk model and in the Euclidean model.

If angles $ (\alpha,\beta,\gamma,\delta) $ are made at points of concurrency $(o,O)$ between lines $(1,2,3,4)$ in either model, then does the same trig definition of Cross Ratio hold good?

If that is so, and if three adjacent angles are given then they have the same Cross Ratio in euclidean and hyperbolic geometries. Is this correct ?