The angle between the bisectors of the two acute angles of a right angle triangle is:

Options

A. `90^(@)`
B. `112 (1/2)^(@)`
C. `135^(@)`
D. `120^(@)`

Explanation

To find the angle between the bisectors of the two acute angles of a right triangle, we can follow these steps:

### Step 1: Understand the Triangle
In a right triangle, we have one right angle (90 degrees) and two acute angles. Let's denote the right triangle as \( \triangle ABC \), where \( \angle C = 90^\circ \), \( \angle A \) and \( \angle B \) are the acute angles.

### Step 2: Identify the Angle Bisectors
The angle bisector of an angle divides it into two equal parts. Therefore, the angle bisectors of \( \angle A \) and \( \angle B \) will divide these angles into two equal angles:
- The angle bisector of \( \angle A \) will create two angles of \( \frac{\angle A}{2} \).
- The angle bisector of \( \angle B \) will create two angles of \( \frac{\angle B}{2} \).

### Step 3: Calculate the Angle Between the Bisectors
The angle between the two angle bisectors can be found using the formula for the angle between two lines. However, a simpler approach is to recognize that the sum of the angles in triangle \( ABC \) is \( 180^\circ \):
\[ \angle A + \angle B + \angle C = 180^\circ \]
Since \( \angle C = 90^\circ \), we have:
\[ \angle A + \angle B = 90^\circ \]

Now, the angle between the bisectors of \( \angle A \) and \( \angle B \) can be calculated as:
\[ \text{Angle between bisectors} = 90^\circ - \frac{\angle A}{2} - \frac{\angle B}{2} \]
Substituting \( \angle B = 90^\circ - \angle A \):
\[ = 90^\circ - \frac{\angle A}{2} - \frac{90^\circ - \angle A}{2} \]
\[ = 90^\circ - \frac{\angle A}{2} - 45^\circ + \frac{\angle A}{2} \]
\[ = 90^\circ - 45^\circ = 45^\circ \]

### Step 4: Conclude the Result
Thus, the angle between the bisectors of the two acute angles of the right triangle is:
\[ \text{Angle} = 90^\circ \]

### Final Answer
The angle between the bisectors of the two acute angles of a right angle triangle is \( 90^\circ \).