Proof: Rearrange Angles

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	m∠FCA = (m∠ACG) + (m∠GCF)	if m∠ACF = (m∠ACG) + (m∠GCF), then m∠FCA = (m∠ACG) + (m∠GCF) (Angle Symmetry Example 2)
2	m∠FCA = (m∠GCF) + (m∠ACG)	if m∠FCA = (m∠ACG) + (m∠GCF), then m∠FCA = (m∠GCF) + (m∠ACG) (Commutative Property Variation 1)
3	m∠GCF = m∠FCG	m∠GCF = m∠FCG (Angle Symmetry Property)
4	m∠FCA = (m∠FCG) + (m∠ACG)	if m∠FCA = (m∠GCF) + (m∠ACG) and m∠GCF = m∠FCG, then m∠FCA = (m∠FCG) + (m∠ACG) (Term 1 Substitution)
5	m∠ACG = m∠GCA	m∠ACG = m∠GCA (Angle Symmetry Property)
6	m∠FCA = (m∠FCG) + (m∠GCA)	if m∠FCA = (m∠FCG) + (m∠ACG) and m∠ACG = m∠GCA, then m∠FCA = (m∠FCG) + (m∠GCA) (Term 2 Substitution)

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