Which term is used to describe the total angle measures in spherical triangles?

The correct term to describe the total angle measures in spherical triangles is known as the spherical sum. In spherical geometry, unlike planar triangles where the sum of the angles is always 180 degrees, the angles in a spherical triangle add up to more than 180 degrees but less than 540 degrees. This excess is due to the curvature of the sphere itself. Each spherical triangle has an angle sum that can be expressed as 180 degrees plus some additional angle, known as the excess angle.

This concept demonstrates a crucial aspect of spherical geometry, showcasing how it diverges from the familiar rules of planar triangles. The spherical sum, therefore, encapsulates the overall angle measurement in spherical triangles and reflects the unique properties that arise from the geometry of the sphere.

While the term "triangular sum" might suggest a summation of angles, it doesn't specifically indicate the unique characteristics of spherical triangles. "Geometric mean" refers to a different mathematical concept not related to angle measures. Lastly, "excess angle" specifically describes the additional portion beyond 180 degrees but does not appropriately encompass the total measure of angles. Thus, "spherical sum" correctly identifies the complete set of angles in spherical triangles.