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

the right answer is becky

Step-by-step explanation:

why is it becky cause angie completed the proof incorrectly

Becky

Step-by-step explanation:

Becky

Step-by-step explanation:

Becky completed the proof incorrectly because her justification for statement 2 is not the right reason why m<AKG + m<GKB = 180°, nor why m<GKB + m<HKB = 180°.

This is rather the definition of supplementary angles.

Angle Addition Postulates holds that the sum of two adjacent angles can be added to give the measure of an unknown angle containing these two adjacent angles. They do not necessarily add up to 189°. Their sum could be less than 180°.

However, supplementary angles definition tells us that if two angles add up to give us 180° they are supplementary. Angles on a straight line are supplementary.

Therefore, Becky completed the proof incorrectly.