The problem involves a rhombus, and we need to find the value of $x$.

Key properties of a rhombus:

1. All sides of a rhombus are equal.
2. The diagonals bisect each other at right angles (90°).
3. The diagonals of a rhombus bisect its internal angles.

Given Information:

• One of the internal angles is marked as 59°.
• The diagonals intersect the internal angles and divide them.
• The angle $x^\circ$ is related to this diagonal property.

Steps to solve:

1. The diagonals bisect the 59° angle. Since diagonals split the angle into two equal parts, each part is: $\frac{59^\circ}{2} = 29.5^\circ$ So, one part of the divided angle is $29.5^\circ$.

2. The diagonal intersects and forms a right angle at the center of the rhombus (90°).

3. The angle $x^\circ$ is formed by a diagonal and part of the bisected angle. Therefore, the total angle $x^\circ$ will be: $x = 90^\circ - 29.5^\circ = 60.5^\circ$

Thus, $x = 60.5^\circ$.

Would you like further clarification or more details on any step?

Here are 5 related questions to deepen your understanding:

1. How do the diagonals of a rhombus relate to its internal angles?
2. Can the interior angles of a rhombus always be divided equally by its diagonals?
3. What is the sum of the interior angles of any quadrilateral?
4. How would the problem change if the rhombus had different angles?
5. How can the properties of a rhombus be applied in solving other geometric shapes?

Tip: Always remember that the diagonals of a rhombus bisect the interior angles, and they are perpendicular to each other!