Find the angle which is four times of its supplementary angle.

Answer

To find the angle which is four times its supplementary angle, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angle**: Let's denote the angle we are trying to find as \( x \). According to the problem, this angle is four times its supplementary angle.

2. **Understand Supplementary Angles**: Supplementary angles are two angles whose sum is \( 180^\circ \). Therefore, if our angle is \( x \), its supplementary angle will be \( 180^\circ - x \).

3. **Set Up the Equation**: According to the problem, we have:
\[ x = 4 \times (180^\circ - x) \]

4. **Expand the Equation**: Now, we can expand the right side of the equation:
\[ x = 720^\circ - 4x \]

5. **Rearrange the Equation**: To solve for \( x \), we can add \( 4x \) to both sides:
\[ x + 4x = 720^\circ \]
This simplifies to:
\[ 5x = 720^\circ \]

6. **Solve for \( x \)**: Now, divide both sides by 5 to find \( x \):
\[ x = \frac{720^\circ}{5} = 144^\circ \]

7. **Conclusion**: The angle which is four times its supplementary angle is \( 144^\circ \).