One angle of a right-angled triangle is `38^(@)`. Find the other angle.

Options

A. `39^(@)`
B. `50^(@)`
C. `52^(@)`
D. `42^(@)`

Answer

To find the other angle in a right-angled triangle where one angle is \(38^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the angles in a right-angled triangle**:
In a right-angled triangle, one angle is always \(90^\circ\). Let's denote the angles as follows:
- Angle A = \(38^\circ\) (given)
- Angle B = \(90^\circ\) (right angle)
- Angle C = ? (the angle we need to find)

2. **Use the angle sum property of triangles**:
The sum of all angles in a 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:
\[ 38^\circ + 90^\circ + \text{Angle C} = 180^\circ \]

3. **Combine the known angles**:
Now, add the angles that we know:
\[ 128^\circ + \text{Angle C} = 180^\circ \]

4. **Solve for Angle C**:
To find Angle C, subtract \(128^\circ\) from \(180^\circ\):
\[ \text{Angle C} = 180^\circ - 128^\circ = 52^\circ \]

5. **Conclusion**:
The other angle in the triangle is \(52^\circ\).

### Final Answer:
The other angle is \(52^\circ\).

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