What is the term for the additional angle that a triangle on a spherical surface has compared to 180 degrees?

The term for the additional angle that a triangle on a spherical surface has compared to 180 degrees is known as spherical excess. In spherical geometry, the sum of the angles in a triangle exceeds 180 degrees due to the curvature of the surface. This additional amount is specifically referred to as the spherical excess, which quantifies how much larger the angles are compared to the planar case.

In practical terms, when dealing with triangles on a sphere, the measurement of spherical excess becomes crucial for accurate calculations in various fields including surveying, navigation, and geodesy. It emphasizes the effect of the Earth's curvature on angle measurement and is foundational in understanding how geometric principles change when applied to non-flat surfaces. This concept is pivotal for students training in surveying, as it impacts how land parcels or features are calculated and represented on maps.