Proof: Supplementary Angles 2

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	∠XYP and ∠PYZ are supplementary	if m∠XYZ = 180, then ∠XYP and ∠PYZ are supplementary (Supplementary Angles Theorem (Converse))
2	(m∠XYP) + (m∠PYZ) = 180	if ∠XYP and ∠PYZ are supplementary, then (m∠XYP) + (m∠PYZ) = 180 (Supplementary Angles Property)
3	m∠PYZ = 90	if ∠PYZ is a right angle, then m∠PYZ = 90 (Right Angle Property)
4	(m∠XYP) + 90 = 180	if (m∠XYP) + (m∠PYZ) = 180 and m∠PYZ = 90, then (m∠XYP) + 90 = 180 (Substitution Example 10)
5	m∠XYP = 180 + (90 ⋅ (-1))	if (m∠XYP) + 90 = 180, then m∠XYP = 180 + (90 ⋅ (-1)) (Add Term to Both Sides 6)
6	m∠XYP = 90	if m∠XYP = 180 + (90 ⋅ (-1)), then m∠XYP = 90 (Subtraction Example 2)

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