Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who completed the proof incorrectly? Explain.


line AB intersecting line GH at K


Angie's Proof



Statement Justification

1. Segment GH intersects segment AB at K 1. Given

2. M∠AKG + m∠GKB = 180°

m∠GKB + m∠HKB = 180° 2. Definition of Supplementary Angles

3. M∠AKG + m∠ GKB = m∠GKB + m∠HKB 3. Substitution Property

4. M∠AKG = m∠HKB 4. Subtraction Property



Becky's Proof


Statement Justification

1. Segment GH intersects segment AB at K 1. Given

2. M∠AKG + m∠GKB = 180°

m∠GKB + m∠HKB = 180° 2. Angle Addition Postulate

3. M∠AKG + m∠ GKB = m∠GKB + m∠HKB 3. Substitution Property

4. M∠AKG = m∠HKB 4. Subtraction Property