Proof: Collinear And One Angle is 90

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	∠ABX and ∠XBC are supplementary	if m∠ABC = 180, then ∠ABX and ∠XBC are supplementary (Supplementary Angles Theorem (Converse))
2	(m∠ABX) + (m∠XBC) = 180	if ∠ABX and ∠XBC are supplementary, then (m∠ABX) + (m∠XBC) = 180 (Supplementary Angles Property)
3	m∠XBA = m∠ABX	m∠XBA = m∠ABX (Angle Symmetry Property)
4	m∠ABX = 90	if m∠XBA = m∠ABX and m∠XBA = 90, then m∠ABX = 90 (Transitive Property of Equality Variation 2)
5	90 + (m∠XBC) = 180	if (m∠ABX) + (m∠XBC) = 180 and m∠ABX = 90, then 90 + (m∠XBC) = 180 (Substitution 8)
6	m∠XBC = 90	if 90 + (m∠XBC) = 180, then m∠XBC = 90 (Add Number to Both Sides 2)

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