Proof: Consecutive Interior Angles Theorem (Converse)

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	m∠XST = m∠STY	if WX || YZ and m∠WSX = 180 and m∠YTZ = 180, then m∠XST = m∠STY (Parallel Then Aia 2)
2	∠WST and ∠TSX are supplementary	if m∠WSX = 180, then ∠WST and ∠TSX are supplementary (Supplementary Angles Theorem (Converse))
3	(m∠WST) + (m∠XST) = 180	if ∠WST and ∠TSX are supplementary, then (m∠WST) + (m∠XST) = 180 (Supplementary Then 180)
4	(m∠WST) + (m∠STY) = 180	if (m∠WST) + (m∠XST) = 180 and m∠XST = m∠STY, then (m∠WST) + (m∠STY) = 180 (Substitution Example 10)
5	∠WST and ∠STY are supplementary	if (m∠WST) + (m∠STY) = 180, then ∠WST and ∠STY are supplementary (Supplementary Angles Property (Converse))

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