A diogonal of a rectangle is inclined to one side of the rectangle at `25^(@)`. The acute angle between the diagonals is

Options

A. `55^(@)`
B. `50^(@)`
C. `40^(@) `
D. `25^(@)`

Explanation

To solve the problem of finding the acute angle between the diagonals of a rectangle when one diagonal is inclined at \(25^\circ\) to one side, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Rectangle and Diagonals**:
- Let the rectangle be \(ABCD\) with diagonals \(AC\) and \(BD\). The diagonals of a rectangle bisect each other and are equal in length.

2. **Identifying the Angles**:
- Given that diagonal \(AC\) is inclined at \(25^\circ\) to side \(AB\), we can denote angle \(CAB = 25^\circ\).

3. **Using Properties of Isosceles Triangles**:
- Since diagonals \(AC\) and \(BD\) bisect each other at point \(O\), triangles \(OAC\) and \(OBD\) are isosceles triangles. Therefore, angles \(OAC\) and \(OCA\) are equal, and angles \(OBD\) and \(ODB\) are equal.

4. **Finding Angles in Triangle \(OAC\)**:
- In triangle \(OAC\), we have:
\[ \angle OAC = \angle OCA = 25^\circ \]
- The sum of angles in triangle \(OAC\) is \(180^\circ\):
\[ \angle AOC + \angle OAC + \angle OCA = 180^\circ \]
\[ \angle AOC + 25^\circ + 25^\circ = 180^\circ \]
\[ \angle AOC = 180^\circ - 50^\circ = 130^\circ \]

5. **Finding the Angle Between the Diagonals**:
- The angle between the diagonals \(AC\) and \(BD\) at point \(O\) is given by:
\[ \angle AOB = \angle AOC = 130^\circ \]
- The acute angle between the diagonals is:
\[ \angle COB = 180^\circ - \angle AOB = 180^\circ - 130^\circ = 50^\circ \]

6. **Final Answer**:
- Therefore, the acute angle between the diagonals of the rectangle is \(50^\circ\).

### Summary
The acute angle between the diagonals of the rectangle is \(50^\circ\).