Find the angle which is three times of its complementary angle.

Answer

To find the angle which is three times its complementary angle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Complementary Angles**:
Complementary angles are two angles whose sum is 90 degrees. If we denote the angle we are trying to find as \( x \), then its complementary angle will be \( 90 - x \).

2. **Set Up the Equation**:
According to the problem, the angle \( x \) is three times its complementary angle. Therefore, we can write the equation:
\[ x = 3(90 - x) \]

3. **Expand the Equation**:
Now, we will expand the right side of the equation:
\[ x = 270 - 3x \]

4. **Combine Like Terms**:
Next, we will add \( 3x \) to both sides to get all terms involving \( x \) on one side:
\[ x + 3x = 270 \]
This simplifies to:
\[ 4x = 270 \]

5. **Solve for \( x \)**:
Now, we will divide both sides by 4 to find the value of \( x \):
\[ x = \frac{270}{4} \]
Simplifying this gives:
\[ x = 67.5 \]

6. **Conclusion**:
The angle which is three times its complementary angle is \( 67.5 \) degrees.