In a rhombus, opposite angles are equal, and adjacent angles are supplementary. This means that:
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For the angles:
- Since \( m\angle DAB = 124° \), we have: \[ m\angle ABC = m\angle DAB = 124° \]
- Thus, \( m\angle ABC = 124° \).
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Calculating the other angles:
- The angles adjacent to \( m\angle DAB \) and \( m\angle ABC \) are supplementary: \[ m\angle ABC + m\angle BCD = 180° \]
- Therefore: \[ m\angle BCD = 180° - 124° = 56° \]
- And since opposite angles in a rhombus are equal: \[ m\angle ABC = m\angle DAB = 124° \quad \text{and} \quad m\angle BCD = m\angle DAB = 56° \]
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Finding angle \( m\angle AEB \):
- The points A, B, D, and E give a diagonal split through vertex angles. The angle \( m\angle AEB \) sits within the triangle ABE formed by the diagonals intersecting at point E.
- In a rhombus, the diagonals bisect the angles: \[ m\angle AEB = \frac{m\angle DAB}{2} = \frac{124°}{2} = 62° \]
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Finding angle \( m\angle ADE \):
- Using the same property of bisected angles, angle \( m\angle ADE \) is half of angle DAB: \[ m\angle ADE = \frac{m\angle DAB}{2} = \frac{124°}{2} = 62° \]
Thus, we can summarize the answers as follows:
- \( m\angle ABC = 56° \)
- \( m\angle AEB = 62° \)
- \( m\angle ADE = 62° \)