To find the measurements of the angles in rhombus ABCD, we can use the properties of rhombuses.
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In a rhombus, all sides are equal, and opposite angles are equal. The sum of the interior angles of any quadrilateral is 360°.
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Given that \( m \angle DAB = 124° \), we know that:
- \( m \angle ABC = 124° \) (since opposite angles in a rhombus are equal)
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To find \( m \angle BCD \) and \( m \angle CDA \):
- Since \( m \angle DAB + m \angle ABC + m \angle BCD + m \angle CDA = 360° \)
- We also know \( m \angle BCD = m \angle CDA \) (since they are opposite angles).
Let \( x = m \angle BCD = m \angle CDA \). Therefore: \[ 124° + 124° + x + x = 360° \] \[ 248° + 2x = 360° \] \[ 2x = 360° - 248° = 112° \] \[ x = 56° \] So, \( m \angle BCD = 56° \) and \( m \angle CDA = 56° \).
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To find \( m \angle AEB \), since E is the intersection of the diagonals of rhombus ABCD, and the diagonals bisect each other at right angles, we can know that:
- Angles \( m \angle AEB = \frac{1}{2} m \angle DAB\) since diagonals bisect the angles.
Therefore, \[ m \angle AEB = \frac{1}{2} \times 124° = 62° \]
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Finally, to find \( m \angle ADE \), we can know that \( m \angle ADE = m \angle CDA \) since they are vertically opposite angles. Thus, \[ m \angle ADE = 56° \]
In summary:
- \( m \angle ABC = 124° \)
- \( m \angle AEB = 62° \)
- \( m \angle ADE = 56° \)