Find the complementary angle of each of the following angles:
`(1)/(3)` right angle

Answer

To find the complementary angle of \( \frac{1}{3} \) of a right angle, follow these steps:

### Step 1: Understand the concept of complementary angles
Complementary angles are two angles whose sum is \( 90^\circ \).

### Step 2: Determine the value of the given angle
The given angle is \( \frac{1}{3} \) of a right angle. A right angle is \( 90^\circ \). Therefore, we can calculate:
\[ x = \frac{1}{3} \times 90^\circ \]

### Step 3: Calculate the value of \( x \)
Now, perform the multiplication:
\[ x = \frac{90}{3} = 30^\circ \]

### Step 4: Use the complementary angle formula
Let \( y \) be the complementary angle. According to the definition of complementary angles:
\[ x + y = 90^\circ \]
We can rearrange this to find \( y \):
\[ y = 90^\circ - x \]

### Step 5: Substitute the value of \( x \) into the equation
Now substitute \( x = 30^\circ \) into the equation:
\[ y = 90^\circ - 30^\circ \]

### Step 6: Calculate the value of \( y \)
Perform the subtraction:
\[ y = 60^\circ \]

### Final Answer
The complementary angle of \( \frac{1}{3} \) of a right angle is \( 60^\circ \).

---