Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who complete
d the proof incorrectly? Explain.
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
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
1 answer:
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Answer:
1.98
Step-by-step explanation:
In this problem, we are:
Given: ∠D = 26°, Hypotenuse (DF) = 4.5
To solve: EF
Now through the given, we are to focus on point D to solve for EF.
We need to find the relationship of point D to DF and EF.
The relationship here is sine.
Reason:
Through point D, DF is the hypotenuse and EF is the opposite side.
So let's solve this simply through algebra,
sin =
sin(26°) =
0.44 =
0.44 × 4.5 = EF
1.98 = EF