Proof: Equal Angles

Let's prove the following theorem:

if m∠AXC = 180 and m∠DCA = m∠CAB, then m∠DCX = m∠XAB

A C X B D

Proof:

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Given
1 m∠AXC = 180
2 m∠DCA = m∠CAB
Proof Table
# Claim Reason
1 m∠DCA = m∠DCX if m∠AXC = 180, then m∠DCA = m∠DCX
2 m∠DCX = m∠CAB if m∠DCA = m∠DCX and m∠DCA = m∠CAB, then m∠DCX = m∠CAB
3 m∠CAB = m∠XAB if m∠AXC = 180, then m∠CAB = m∠XAB
4 m∠DCX = m∠XAB if m∠DCX = m∠CAB and m∠CAB = m∠XAB, then m∠DCX = m∠XAB

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