Given that the angle sum of a triangle made of great circle arcs on a sphere (a spherical triangle)...

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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 degrees. 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.
	
Document Preview: 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 degrees. 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.

Robert · Accepted Answer

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 degrees.

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...

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