(4) We commented that we thought that every spherical triangle should have angle sum bigger than...

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(4) We commented that we thought that every spherical triangle should have angle sum bigger than 180°. Show (intuitively) that the angle excess, the amount by which the angle-sum of a triangle is bigger than 180°, is additive when triangles are placed side-by-side. That is, in the diagram below: A Show that D the angle excess of AABC is excess(AABC) = m/ABC + m2BCA +mZCAB - 180°. excess(AADB) + excess(ADCB) = excess(ABC) (4) We commented that we thought that every spherical triangle should have angle sum bigger than 180°. Show (intuitively) that the angle excess, the amount by which the angle-sum of a triangle is bigger than 180°, is additive when triangles are placed side-by-side. That is, in the diagram below: A Show that D the angle excess of AABC is excess(AABC) = m/ABC + m2BCA +mZCAB - 180°. excess(AADB) + excess(ADCB) = excess(ABC)

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