One of the acute angles of a right triangle is `36^(@)`,find the other `

Options

A. `54^@`
B. `50^@`
C. `60^@`
D. `65^@`

Answer

To find the other acute angle in a right triangle where one acute angle is given as \(36^\circ\), 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 the angles in any triangle is \(180^\circ\).

2. **Identify the angles**: Let’s denote the angles in the triangle as follows:
- Angle A = \(36^\circ\) (given)
- Angle B = \(90^\circ\) (the right angle)
- Angle C = the angle we need to find.

3. **Set up the equation for the sum of angles**: According to the triangle angle sum property:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
Substituting the known values:
\[ 36^\circ + 90^\circ + \text{Angle C} = 180^\circ \]

4. **Combine the known angles**: Add \(36^\circ\) and \(90^\circ\):
\[ 126^\circ + \text{Angle C} = 180^\circ \]

5. **Solve for Angle C**: To find Angle C, subtract \(126^\circ\) from \(180^\circ\):
\[ \text{Angle C} = 180^\circ - 126^\circ = 54^\circ \]

6. **Conclusion**: The other acute angle in the triangle is \(54^\circ\).

### Final Answer:
The other acute angle is \(54^\circ\).

---