Which term describes the difference between the angles of a plane triangle and a spherical triangle?

• A. Spherical excess
• B. Angle of repose
• C. Geoid
• D. Magnetic declination

Answer: (A)

Spherical excess is the term that specifically refers to the difference between the sum of the angles of a spherical triangle and the sum of the angles of a plane triangle. In a plane triangle, the sum of the angles is always exactly 180 degrees. However, in a spherical triangle, formed by great circle arcs on the surface of a sphere, the sum of the angles exceeds 180 degrees. The amount by which it exceeds 180 degrees is defined as the spherical excess, and it is a fundamental concept in spherical geometry and geodesy, particularly useful in surveying and navigation.

Other terms such as angle of repose, geoid, and magnetic declination do not relate to the comparison of angles in triangles. Angle of repose pertains to the steepest angle at which material can exist in a stable condition without sliding. Geoid refers to the Earth's mean sea level shape, considering gravitational variations. Magnetic declination involves the angle between magnetic north and true north. Thus, only spherical excess accurately describes the concept stated in the question.