Proof: Third Angle Theorem

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	((m∠ABC) + (m∠BCA)) + (m∠CAB) = 180	((m∠ABC) + (m∠BCA)) + (m∠CAB) = 180 (triangles_sum_to_180)
2	(m∠ABC) + (m∠BCA) = (m∠XYZ) + (m∠YZX)	if m∠ABC = m∠XYZ and m∠BCA = m∠YZX, then (m∠ABC) + (m∠BCA) = (m∠XYZ) + (m∠YZX) (Equality Example)
3	((m∠XYZ) + (m∠YZX)) + (m∠CAB) = 180	if ((m∠ABC) + (m∠BCA)) + (m∠CAB) = 180 and (m∠ABC) + (m∠BCA) = (m∠XYZ) + (m∠YZX), then ((m∠XYZ) + (m∠YZX)) + (m∠CAB) = 180 (Substitution 8)
4	m∠CAB = 180 + (((m∠XYZ) + (m∠YZX)) ⋅ (-1))	if ((m∠XYZ) + (m∠YZX)) + (m∠CAB) = 180, then m∠CAB = 180 + (((m∠XYZ) + (m∠YZX)) ⋅ (-1)) (Add Term to Both Sides 7)
5	((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180	((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180 (triangles_sum_to_180)
6	m∠ZXY = 180 + (((m∠XYZ) + (m∠YZX)) ⋅ (-1))	if ((m∠XYZ) + (m∠YZX)) + (m∠ZXY) = 180, then m∠ZXY = 180 + (((m∠XYZ) + (m∠YZX)) ⋅ (-1)) (Add Term to Both Sides 7)
7	m∠CAB = m∠ZXY	if m∠CAB = 180 + (((m∠XYZ) + (m∠YZX)) ⋅ (-1)) and m∠ZXY = 180 + (((m∠XYZ) + (m∠YZX)) ⋅ (-1)), then m∠CAB = m∠ZXY (Transitive Property of Equality Variation 1)

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