Proof: Vertical Angles Apply

Let's prove the following theorem:

if m∠WSX = 180 and m∠YSZ = 180 and ray SX bisects ∠TSZ, then m∠WSY = m∠TSX

W Z Y X S T

Proof:

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Given
1 m∠WSX = 180
2 m∠YSZ = 180
3 ray SX bisects ∠TSZ
Proof Table
# Claim Reason
1 m∠TSX = m∠XSZ if ray SX bisects ∠TSZ, then m∠TSX = m∠XSZ
2 m∠XSZ = m∠WSY if m∠WSX = 180 and m∠YSZ = 180, then m∠XSZ = m∠WSY
3 m∠WSY = m∠TSX if m∠TSX = m∠XSZ and m∠XSZ = m∠WSY, then m∠WSY = m∠TSX

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