O = is the center of the sphere, and ABC is a spherical right triangle on the sphere's surface. There are 120 of these triangles (60 left and 60 right) on the surface of the Great Circle Challenge.
Basic angles of the spherical right triangle: A= 60 degrees, B = 90 degrees, C = 36 degrees, Total of all three angles of this spherical right triangle = 186 degrees. Unlike right triangles on a flat surface, spherical right triangles will add up to more then 180 degrees. As the triangle gets larger (it covers a greater surface area on the sphere) the greater the total of the three angles of the triangle becomes.
In fact you can always look at the triangle as having two sets of angles, those on the “inside” of the triangle and those on the “outside” of the triangle. The outside angles call them A’, B’, and C’ (in the example above) would be A’ = 300 degrees, B’ = 270 degrees, and C’ = 324 degrees, with a total of all three “outside” angles = 894 degrees. If you add up the “inside” angle and the “outside” angles of any triangle on the surface of a sphere they will always equal 1080 degrees which equals 360 degrees times 3.
If you draw a radius line from the center of the sphere to the end points of a line drawn on the surface of a sphere you will create an arc angle (the angle between the two lines drawn from the center point to the lines end points). On the diagram above these angles AOB = 29.9 degrees, AOC = 37.4 degrees, and BOC = 31.7 degrees.
