Given that the angle sum of a triangle made of great ci

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.
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