In Euclidean geometry, the sum of the measures of the interior angles of a pentagon is 540°. Predict how the sum of the measures of the interior angles of a pentagon would be different in spherical geometry.

Question

dumbcow · Answer

It depends how much area the pentagon takes up on the surface of the sphere

$$Sum = 3\pi + Area$$

i converted to radians because area in spherical geometry is in terms of pi

dumbcow · Answer

https://en.wikipedia.org/wiki/Spherical_trigonometry#Area_and_spherical_excess