Proof: Supplementary Angles Theorem (Converse)

Let's prove the following theorem:

if m∠ABC = 180, then ∠ABX and ∠XBC are supplementary

X A B C

Proof:

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Given
1 m∠ABC = 180
Proof Table
# Claim Reason
1 (m∠ABX) + (m∠XBC) = 180 if m∠ABC = 180, then (m∠ABX) + (m∠XBC) = 180
2 ∠ABX and ∠XBC are supplementary if (m∠ABX) + (m∠XBC) = 180, then ∠ABX and ∠XBC are supplementary

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