Supplementary Angles Theorem

Proof: Supplementary Angles Theorem

Let's prove the following theorem:

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

X A B C

Proof:

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

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