Proof: Exterior Angle Equal to Sum of Nonadjacent

Let's prove the following theorem:

if m∠XYZ = 180, then m∠WYZ = (m∠WXY) + (m∠YWX)

Proof:

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Given

1	m∠XYZ = 180

Proof Table

#	Claim	Reason
1	((m∠WXY) + (m∠XYW)) + (m∠YWX) = 180	((m∠WXY) + (m∠XYW)) + (m∠YWX) = 180 (triangles_sum_to_180)
2	(m∠XYW) + (m∠WYZ) = 180	if m∠XYZ = 180, then (m∠XYW) + (m∠WYZ) = 180 (Collinear Points Theorem)
3	(m∠WXY) + (m∠YWX) = 180 + ((m∠XYW) ⋅ (-1))	if ((m∠WXY) + (m∠XYW)) + (m∠YWX) = 180, then (m∠WXY) + (m∠YWX) = 180 + ((m∠XYW) ⋅ (-1)) (Reorder Terms 4)
4	m∠WYZ = 180 + ((m∠XYW) ⋅ (-1))	if (m∠XYW) + (m∠WYZ) = 180, then m∠WYZ = 180 + ((m∠XYW) ⋅ (-1)) (Add Term to Both Sides 7)
5	m∠WYZ = (m∠WXY) + (m∠YWX)	if m∠WYZ = 180 + ((m∠XYW) ⋅ (-1)) and (m∠WXY) + (m∠YWX) = 180 + ((m∠XYW) ⋅ (-1)), then m∠WYZ = (m∠WXY) + (m∠YWX) (Transitive Property of Equality Variation 1)

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