In the diagram above, quadrilateral ABCD is a rhombus. If the m ∠DAB

Question

= 124 °
find the measurements below.

(3 points)
m∠ABC= solve it correctly and carefully to get 100 on your test

°

m∠AEB=

°

m∠ADE=

Answer 1

In a rhombus, the following properties hold:

1. All sides are equal in length.
2. Opposite angles are equal.
3. The diagonals bisect each other at right angles.
4. The sum of the angles in any quadrilateral is 360°.

Given that \( m \angle DAB = 124° \), we can find the other angles.

1. Since opposite angles are equal in a rhombus, we have: \[ m \angle BCD = m \angle DAB = 124° \]

2. The adjacent angles in a rhombus are supplementary (they add up to 180°): \[ m \angle ABC + m \angle DAB = 180° \] Thus, \[ m \angle ABC = 180° - 124° = 56° \]

3. Since angles \( AEB \) and \( ADE \) correspond to angles formed by the intersection of the diagonals of the rhombus, note that diagonals bisect the angles. Thus, we can find \( m \angle AEB \) and \( m \angle ADE \).

   Diagonal \( AC \) bisects angle \( \angle DAB \): \[ m \angle AEB = \frac{m \angle DAB}{2} = \frac{124°}{2} = 62° \]

   Similarly, diagonal \( BD \) bisects angle \( ABC \): \[ m \angle ADE = \frac{m \angle ABC}{2} = \frac{56°}{2} = 28° \]

To summarize:

• \( m \angle ABC = 56° \)
• \( m \angle AEB = 62° \)
• \( m \angle ADE = 28° \)

Final Answers:

• \( m \angle ABC = 56° \)
• \( m \angle AEB = 62° \)
• \( m \angle ADE = 28° \)