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Question
In the diagram above, quadrilateral ABCD is a rhombus. If the m∠DAB
= 124°
find the measurements below.
(3 points)
m∠ABC=
°
m∠AEB=
°
m∠ADE=
°
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Answers
GPT-4o mini
In a rhombus, we know the following properties:
1. All sides are of equal length.
2. Opposite angles are equal.
3. The sum of angles in any quadrilateral is 360°.
4. Adjacent angles are supplementary (they add up to 180°).
Given that \( m∠DAB = 124° \):
1. To find \( m∠ABC \):
- Since \( m∠DAB \) and \( m∠ABC \) are opposite angles in the rhombus, they are equal.
- Thus, \( m∠ABC = 124° \).
2. To find \( m∠AEB \):
- Since \( m∠DAB + m∠ABC = 180° \) (adjacent angles in the rhombus),
- We have \( m∠AEB = 180° - m∠DAB = 180° - 124° = 56° \).
3. To find \( m∠ADE \):
- \( m∠ADE \) is another adjacent angle to \( m∠DAB \) and is equal to \( m∠ABC \) because they are opposite angles.
- Thus, \( m∠ADE = m∠ABC = 124° \).
Final Measurements:
- \( m∠ABC = 124° \)
- \( m∠AEB = 56° \)
- \( m∠ADE = 124° \)
1. All sides are of equal length.
2. Opposite angles are equal.
3. The sum of angles in any quadrilateral is 360°.
4. Adjacent angles are supplementary (they add up to 180°).
Given that \( m∠DAB = 124° \):
1. To find \( m∠ABC \):
- Since \( m∠DAB \) and \( m∠ABC \) are opposite angles in the rhombus, they are equal.
- Thus, \( m∠ABC = 124° \).
2. To find \( m∠AEB \):
- Since \( m∠DAB + m∠ABC = 180° \) (adjacent angles in the rhombus),
- We have \( m∠AEB = 180° - m∠DAB = 180° - 124° = 56° \).
3. To find \( m∠ADE \):
- \( m∠ADE \) is another adjacent angle to \( m∠DAB \) and is equal to \( m∠ABC \) because they are opposite angles.
- Thus, \( m∠ADE = m∠ABC = 124° \).
Final Measurements:
- \( m∠ABC = 124° \)
- \( m∠AEB = 56° \)
- \( m∠ADE = 124° \)