How many degrees are there in an angle which equals one - fifth of its supplement ?

Options

A. `15^(@)`
B. `30^(@)`
C. `75^(@)`
D. `150^(@)`

Answer

To solve the problem of finding an angle that equals one-fifth of its supplement, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Supplementary Angles**:
- Two angles are supplementary if their sum is 180 degrees. If we denote our angle as \( x \), then its supplement will be \( 180 - x \).

2. **Set Up the Equation**:
- According to the problem, the angle \( x \) is equal to one-fifth of its supplement. Therefore, we can express this relationship as:
\[ x = \frac{1}{5} \times (180 - x) \]

3. **Multiply Both Sides by 5**:
- To eliminate the fraction, multiply both sides of the equation by 5:
\[ 5x = 180 - x \]

4. **Rearrange the Equation**:
- Add \( x \) to both sides to combine like terms:
\[ 5x + x = 180 \]
\[ 6x = 180 \]

5. **Solve for \( x \)**:
- Divide both sides by 6 to find the value of \( x \):
\[ x = \frac{180}{6} = 30 \]

6. **Conclusion**:
- The angle \( x \) is 30 degrees. Therefore, the angle that equals one-fifth of its supplement is:
\[ \text{Angle} = 30 \text{ degrees} \]