Proof: Collinear Points

Let's prove the following theorem:

if m∠DBX = m∠CAY and m∠AXB = 180 and m∠AYB = 180, then m∠DBA = m∠CAB

A B X Y C D

Proof:

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Given
1 m∠DBX = m∠CAY
2 m∠AXB = 180
3 m∠AYB = 180
Proof Table
# Claim Reason
1 m∠DBX = m∠DBA if m∠AXB = 180, then m∠DBX = m∠DBA
2 m∠CAY = m∠CAB if m∠AYB = 180, then m∠CAY = m∠CAB
3 m∠DBA = m∠CAB if m∠DBX = m∠CAY and m∠DBX = m∠DBA and m∠CAY = m∠CAB, then m∠DBA = m∠CAB

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