2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58260We consider the rational linear relations between real numbers whose squared trigonometric functions have rational values, angles we call ``geodetic''. We construct a convenient basis for the vector space over Q generated by these angles. Geodetic angles and rational linear combinations of geodetic angles appear naturally in Euclidean geometry; for illustration we apply our results to equidecomposability of polyhedra.Plain TeX. 16 pages including two embedded postscript figuresMathematical PhysicsMetric GeometryNumber Theory52B60 (Primary) 52C20, 05B45, 82B0 (Secondary)text