  Around 1930, K. Menger expressed his interest in the concept of abstract
angle function. He introduced a general definition of this notion for metric
and semi-metric spaces. He also proposed two problems concerning conformal
embeddability of spaces endowed with an angle function into Euclidean spaces.
These problems received attention in later years but only for some particular
cases of metric spaces. In this article we first update the definition of angle
function to apply to the larger class of spaces with a notion of betweenness,
which seem to us a more natural framework. In this new general setting, we
solve the two problems proposed by Menger.
