In a rhombus, all sides are equal and the opposite angles are equal. The adjacent angles in a rhombus are supplementary—for example, the angles \( \angle DAB \) and \( \angle ABC \) are adjacent angles.
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Given that \( m \angle DAB = 124^\circ \): \[ m \angle ABC = 180^\circ - m \angle DAB = 180^\circ - 124^\circ = 56^\circ \]
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Since \( A, B \) are vertices and \( E \) is the intersection point of the diagonals of the rhombus, the diagonals bisect each other at right angles. Hence, triangle \( AEB \) is isosceles and we know \( \angle DAB \) is bisected into two equal angles at point E, meaning: \[ m \angle AEB = 180^\circ - m \angle DAB = 180^\circ - 124^\circ = 56^\circ \]
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Finally, \( \angle ADE \) is equal to \( m \angle DAB \) because opposite angles are equal in a rhombus: \[ m \angle ADE = m \angle DAB = 124^\circ \]
Bringing all of this together, we have:
- \( m \angle ABC = 56^\circ \)
- \( m \angle AEB = 56^\circ \)
- \( m \angle ADE = 124^\circ \)
So, the final answers are:
- \( m \angle ABC = 56^\circ \)
- \( m \angle AEB = 56^\circ \)
- \( m \angle ADE = 124^\circ \)