Proof: Vertical Angles 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	∠WPZ and ∠ZPY are supplementary	if m∠WPY = 180, then ∠WPZ and ∠ZPY are supplementary (Supplementary Angles Theorem (Converse))
2	(m∠WPZ) + (m∠ZPY) = 180	if ∠WPZ and ∠ZPY are supplementary, then (m∠WPZ) + (m∠ZPY) = 180 (Supplementary Angles Property)
3	m∠ZPY = 180 + ((m∠WPZ) ⋅ (-1))	if (m∠WPZ) + (m∠ZPY) = 180, then m∠ZPY = 180 + ((m∠WPZ) ⋅ (-1)) (Add Term to Both Sides 7)
4	∠XPW and ∠WPZ are supplementary	if m∠XPZ = 180, then ∠XPW and ∠WPZ are supplementary (Supplementary Angles Theorem (Converse))
5	(m∠XPW) + (m∠WPZ) = 180	if ∠XPW and ∠WPZ are supplementary, then (m∠XPW) + (m∠WPZ) = 180 (Supplementary Angles Property)
6	m∠XPW = 180 + ((m∠WPZ) ⋅ (-1))	if (m∠XPW) + (m∠WPZ) = 180, then m∠XPW = 180 + ((m∠WPZ) ⋅ (-1)) (Add Term to Both Sides 6)
7	m∠ZPY = m∠XPW	if m∠ZPY = 180 + ((m∠WPZ) ⋅ (-1)) and m∠XPW = 180 + ((m∠WPZ) ⋅ (-1)), then m∠ZPY = m∠XPW (Transitive Property of Equality Variation 1)

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