A least squares equation expressing that the three measured angles of a triangle must equal 180 degrees plus the spherical excess of the triangle is known as which type of equation?

• A. condition
• B. residual
• C. normal
• D. observation

Answer: (A)

A constraint on the unknowns is expressed as a condition equation. In a least-squares framework, such equations impose fixed relationships between quantities that must hold for any feasible solution, beyond what individual observations provide. The sum of the three angles being 180 degrees plus the spherical excess is exactly this kind of global geometric link, tying the angles together in a rule that must be satisfied. A residual would be the difference between an observed value and its computed counterpart for one measurement, which this equation is not; a normal equation comes from optimizing the sum of squared residuals to solve for the unknowns, and an observation is simply a measured value. So this equation is best described as a condition equation.