Proof: Vertical Angles

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(m∠XPY) + (m∠YPW) = 180	if m∠XPW = 180, then (m∠XPY) + (m∠YPW) = 180 (Collinear Points Theorem)
2	m∠XPY = 180 + ((m∠YPW) ⋅ (-1))	if (m∠XPY) + (m∠YPW) = 180, then m∠XPY = 180 + ((m∠YPW) ⋅ (-1)) (Add Term to Both Sides 6)
3	(m∠YPW) + (m∠WPZ) = 180	if m∠YPZ = 180, then (m∠YPW) + (m∠WPZ) = 180 (Collinear Points Theorem)
4	m∠WPZ = 180 + ((m∠YPW) ⋅ (-1))	if (m∠YPW) + (m∠WPZ) = 180, then m∠WPZ = 180 + ((m∠YPW) ⋅ (-1)) (Add Term to Both Sides 7)
5	m∠WPZ = m∠XPY	if m∠WPZ = 180 + ((m∠YPW) ⋅ (-1)) and m∠XPY = 180 + ((m∠YPW) ⋅ (-1)), then m∠WPZ = m∠XPY (Transitive Property of Equality Variation 1)

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