1. Introduction. In a series of articles on metrical geometry f Menger has made a study of the geometry of certain abstract metric spaces and in particular he has obtained conditions for the congruence of metric spaces with sub-sets of euclidean spaces. In a recent article^ he suggests a system of axioms for "angle spaces" and related problems. It will be shown in this note that a theory of angles analogous to that of euclidean space is possible for convex complete metric spaces any four points

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... of which are congruent with four points in some euclidean space. From this certain theorems regarding tangents to simple arcs are deduced.