This Demonstration shows a spherical triangle. Three 2D sliders on the left control the vertices with spherical coordinates and sliding horizontally from 0 to 360° and vertically from 0 to 180°, respectively.
Geometry on a sphere is a noneuclidean geometry. Straight lines are represented as great circles and edges of a spherical triangle are parts of these great circles. The sum of the angles of a spherical triangle is always greater than 180°.
Snapshot 1: vertices close together form a triangle with the sum of its angles close to 180°
Snapshot 2: a triangle with three right angles, with angle a sum equal to 270°
Snapshot 3: all vertices lying on one great circle give an angle sum of 540°