Each acute angle of an isosceles right triangle measures `60^(@)`.

Answer

To solve the problem, we need to analyze the properties of an isosceles right triangle and the angles involved.

### Step-by-Step Solution:

1. **Understanding the Triangle**:
An isosceles right triangle has two equal sides and one right angle (90 degrees). The two equal angles are the acute angles.

2. **Identifying the Angles**:
In an isosceles right triangle, the angles are denoted as follows:
- Let angle A = angle C (the two equal acute angles)
- Let angle B = 90 degrees (the right angle)

3. **Using the Triangle Angle Sum Property**:
The sum of all angles in a triangle is always 180 degrees. Therefore, we can write the equation:
\[ \text{angle A} + \text{angle B} + \text{angle C} = 180^\circ \]

4. **Substituting the Known Values**:
Since angle A = angle C, we can denote them as x:
\[ x + 90^\circ + x = 180^\circ \]

5. **Simplifying the Equation**:
Combine like terms:
\[ 2x + 90^\circ = 180^\circ \]

6. **Isolating x**:
Subtract 90 degrees from both sides:
\[ 2x = 180^\circ - 90^\circ \]
\[ 2x = 90^\circ \]

7. **Dividing by 2**:
To find x, divide both sides by 2:
\[ x = \frac{90^\circ}{2} = 45^\circ \]

8. **Conclusion**:
Therefore, each acute angle in an isosceles right triangle measures 45 degrees, not 60 degrees.

### Final Answer:
Each acute angle of an isosceles right triangle measures \( 45^\circ \).