# Thread: excess of a triangle

1. ## excess of a triangle

Given that the angle sum of a triangle made of great circle arcs on a sphere (a spherical triangle) is greater than two right angles, define the excess of a triangle as the difference between its angle sum and 180°.Show that if a spherical triangle ABC is split into two triangles by an arc BD from vertex B to the opposite side, then the excess of triangle ABC is equal to the sum of the excesses of triangles ABD and BDC.

2. ## Re: excess of a triangle

Originally Posted by henderson7878
Given that the angle sum of a triangle made of great circle arcs on a sphere (a spherical triangle) is greater than two right angles, define the excess of a triangle as the difference between its angle sum and 180°.Show that if a spherical triangle ABC is split into two triangles by an arc BD from vertex B to the opposite side, then the excess of triangle ABC is equal to the sum of the excesses of triangles ABD and BDC.
What have you been able to do with this?

-Dan