Proof: Two Collinear Angles

Let's prove the following theorem:

if m∠ABC = 180 and m∠IJK = 180 and m∠XCA = m∠YKI, then m∠XCB = m∠YKJ

A B C I J K X Y

Proof:

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Given
1 m∠ABC = 180
2 m∠IJK = 180
3 m∠XCA = m∠YKI
Proof Table
# Claim Reason
1 m∠XCA = m∠XCB if m∠ABC = 180, then m∠XCA = m∠XCB
2 m∠YKI = m∠YKJ if m∠IJK = 180, then m∠YKI = m∠YKJ
3 m∠XCB = m∠YKJ if m∠XCA = m∠YKI and m∠XCA = m∠XCB and m∠YKI = m∠YKJ, then m∠XCB = m∠YKJ

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