State which of the following statements are true and which are false :
In a right angled triangle, the sum of two acute angles is `90^(@)`

Answer

To determine whether the statement "In a right-angled triangle, the sum of two acute angles is 90 degrees" is true or false, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of a Right-Angled Triangle**:
A right-angled triangle is a triangle that has one angle measuring 90 degrees.

2. **Identify the Angles in a Right-Angled Triangle**:
Let's denote the angles of the triangle as A, B, and C. In a right-angled triangle, we can assume:
- Angle A = 90 degrees (the right angle)
- Angles B and C are the other two angles, which are acute angles.

3. **Use the Triangle Sum Property**:
According to the triangle sum property, the sum of all angles in a triangle is always 180 degrees. Therefore, we can write:
\[ A + B + C = 180 \text{ degrees} \]
Since we know that \( A = 90 \text{ degrees} \), we can substitute this into the equation:
\[ 90 + B + C = 180 \]

4. **Solve for the Sum of Angles B and C**:
To find the sum of angles B and C, we can rearrange the equation:
\[ B + C = 180 - 90 \]
\[ B + C = 90 \text{ degrees} \]

5. **Conclusion**:
Since we have shown that the sum of the two acute angles (B and C) in a right-angled triangle is indeed 90 degrees, we can conclude that the statement is true.

### Final Answer:
The statement "In a right-angled triangle, the sum of two acute angles is 90 degrees" is **True**.

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