One of the acute angles of a right triangle is `50^(@)`. Find the other acute angle.

Options

A. `40^(@)`
B. `50^(@)`
C. `60^(@)`
D. `70^(@)`

Answer

To find the other acute angle of a right triangle when one acute angle is given as \(50^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the properties of a right triangle**: In a right triangle, one angle is always \(90^\circ\) (the right angle), and the sum of all angles in any triangle is \(180^\circ\).

2. **Identify the angles**: Let’s denote the angles of the triangle as:
- Angle A = \(50^\circ\) (given acute angle)
- Angle B = \(90^\circ\) (the right angle)
- Angle C = the angle we need to find (the other acute angle)

3. **Set up the equation**: According to the triangle angle sum property:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
Substituting the known values:
\[ 50^\circ + 90^\circ + \text{Angle C} = 180^\circ \]

4. **Combine the known angles**: Add \(50^\circ\) and \(90^\circ\):
\[ 50^\circ + 90^\circ = 140^\circ \]
So the equation becomes:
\[ 140^\circ + \text{Angle C} = 180^\circ \]

5. **Solve for Angle C**: To find Angle C, subtract \(140^\circ\) from \(180^\circ\):
\[ \text{Angle C} = 180^\circ - 140^\circ = 40^\circ \]

6. **Conclusion**: The other acute angle of the triangle is \(40^\circ\).

### Final Answer:
The other acute angle is \(40^\circ\).

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