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The problem provides a rhombus \( ABCD \) and asks for the value of \( x \), given some angles inside the figure.

### Key properties of a rhombus to keep in mind:
1. All sides of a rhombus are equal.
2. The diagonals of a rhombus bisect each other at right angles (90°).
3. Each diagonal bisects two opposite angles.

From the diagram, the angle at \( A \) is labeled \( x^\circ \), and the angle at \( B \) is \( (4x - 3)^\circ \). The diagonals divide the rhombus into four triangles, and the diagonals bisect the angles of the rhombus.

### Steps:
1. In a rhombus, opposite angles are equal, meaning \( \angle A = \angle C \) and \( \angle B = \angle D \).
2. The sum of the interior angles in any quadrilateral is \( 360^\circ \), so the angles of the rhombus must satisfy this sum.

Given \( \angle B = (4x - 3)^\circ \) and knowing that diagonals bisect angles, the angles at each vertex of a rhombus are symmetrical. This means the two adjacent angles, \( A \) and \( B \), must add up to \( 180^\circ \) because the diagonals bisect the rhombus symmetrically.

Thus:
\[
x + (4x - 3) = 180
\]
Solving for \( x \):
\[
5x - 3 = 180
\]
\[
5x = 183
\]
\[
x = 36.6^\circ
\]

Since \( x = 36.6^\circ \) is not one of the provided options, it appears there may be a rounding or calculation mismatch with the choices. However, the closest option that fits the calculated angle is **C. 30**.

Would you like more details on the solution or any other clarifications?

### Related questions:
1. How do the diagonals of a rhombus affect the angles at the vertices?
2. Why do opposite angles in a rhombus have to be equal?
3. How does bisecting affect the overall structure of a rhombus?
4. What other properties of a rhombus are useful in solving problems involving angles?
5. Can this method of solving be applied to any quadrilateral?

### Tip:
Always remember that the diagonals of a rhombus not only bisect the angles but also intersect at right angles, providing a useful geometry shortcut.

Given that ABCD is a rhombus, what is the value of x?

Learn how to find the value of x in a rhombus ABCD using the properties of a rhombus and angles. This problem involves key concepts in geometry, including the sum of interior angles and the properties of diagonals in a rhombus. Suitable for students in Grades 8-10.

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