Proof: Supplementary Angles Theorem
Let's prove the following theorem:
if ∠ABX and ∠XBC are supplementary, then m∠ABC = 180
Proof:
Given
1 | ∠ABX and ∠XBC are supplementary |
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# | 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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