One of the acute angles of a right-angled triangle measures `30^(@)`. What is the measure of the other acute angle ?

Answer

To find the measure of the other acute angle in a right-angled triangle when one of the acute angles measures \(30^\circ\), follow these steps:

### Step-by-Step Solution:

1. **Understand the Triangle**: In a right-angled triangle, one angle is always \(90^\circ\). Let's denote the angles of the triangle as follows:
- Angle \(A\) (acute angle) = \(30^\circ\)
- Angle \(B\) (right angle) = \(90^\circ\)
- Angle \(C\) (the other acute angle) = ?

2. **Use the Angle Sum Property**: The sum of all angles in any triangle is \(180^\circ\). Therefore, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
Substituting the known values:
\[ 30^\circ + 90^\circ + \text{Angle C} = 180^\circ \]

3. **Combine the Known Angles**: Add the angles we know:
\[ 30^\circ + 90^\circ = 120^\circ \]
So the equation now looks like:
\[ 120^\circ + \text{Angle C} = 180^\circ \]

4. **Solve for Angle C**: To find Angle C, subtract \(120^\circ\) from both sides of the equation:
\[ \text{Angle C} = 180^\circ - 120^\circ \]
\[ \text{Angle C} = 60^\circ \]

5. **Conclusion**: The measure of the other acute angle is \(60^\circ\).

### Final Answer:
The measure of the other acute angle is \(60^\circ\).