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This problem involves finding the angles in a rhombus with given diagonal properties.

### Key information:
1. The rhombus is split by diagonals, which meet at a right angle (90°).
2. One of the angles is given as 53°.

### Steps to Solve:

1. **Angle at the intersection of diagonals**: Diagonals of a rhombus bisect each other perpendicularly, meaning the angles they form at the intersection are always 90°.
   - Thus, \( \angle 3 = 90^\circ \).

2. **Using the property of the rhombus**: Diagonals bisect opposite angles equally. So, each angle of the rhombus will be split into two equal parts by the diagonals.

3. **Given angle \( \angle 2 = 53^\circ \)**: This is half of the total angle at the vertex between sides 2 and 4.
   - Therefore, the total angle at that vertex is \( 2 \times 53^\circ = 106^\circ \).
   - This also means \( m\angle 1 = 106^\circ \), because diagonals bisect angles of a rhombus equally.

4. **Remaining angles**: The other two angles (where sides 1 and 3 meet) must be supplementary to \( 106^\circ \), meaning they sum to \( 180^\circ \) with it. 
   - The total opposite angle is \( 180^\circ - 106^\circ = 74^\circ \).
   - Since diagonals bisect the angles, \( \angle 4 = \frac{74^\circ}{2} = 37^\circ \).

### Final Angle Measures:
- \( m\angle 1 = 106^\circ \)
- \( m\angle 2 = 53^\circ \)
- \( m\angle 3 = 90^\circ \)
- \( m\angle 4 = 37^\circ \)

Let me know if you'd like further explanation! Here are some related questions:

1. What are the properties of the diagonals of a rhombus?
2. How do the diagonals of a rhombus bisect angles?
3. Why are diagonals in a rhombus perpendicular?
4. How can supplementary angles help in finding unknown angles in polygons?
5. How do you calculate angles in other quadrilaterals with diagonals?

**Tip**: In any rhombus, the diagonals bisect each other at 90°, a useful property for calculating angles.

For the rhombus shown, find the measures of ∠1, ∠2, ∠3, and ∠4.

This problem involves calculating the measures of four angles in a rhombus using properties of diagonals and angle relationships. The diagonals bisect the angles and intersect at right angles. Given ∠2 = 53°, find m∠1, m∠2, m∠3, and m∠4 with a step-by-step solution.

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