Angle Addition Theorem
Angle Addition Theorem 2

Proof: Angle Addition Theorem

Let's prove the following theorem:

if point X lies in interior of ∠ABC, then m∠ABC = (m∠ABX) + (m∠XBC)

A C B X

Proof:

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Given
1 point X lies in interior of ∠ABC
Proof Table
# Claim Reason
1 ((m∠ABX) + (m∠XBC) < 180) or ((m∠ABX) + (m∠XBC) = 180) if point X lies in interior of ∠ABC, then ((m∠ABX) + (m∠XBC) < 180) or ((m∠ABX) + (m∠XBC) = 180)
2 m∠ABC = (m∠ABX) + (m∠XBC) if ((m∠ABX) + (m∠XBC) < 180) or ((m∠ABX) + (m∠XBC) = 180), then m∠ABC = (m∠ABX) + (m∠XBC)
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