Understanding the Problem
To find an angle that is four times its supplement, we first need to understand the concept of supplementary angles. Two angles are supplementary if the sum of their measures is 180 degrees.

Defining the Variables
- Let the angle be represented as \( x \).
- The supplement of the angle is \( 180 - x \).

Setting Up the Equation
According to the problem, the angle \( x \) is four times its supplement:
- \( x = 4(180 - x) \)

Simplifying the Equation
Now, let's simplify this equation step-by-step:
1. Expand the right side:
- \( x = 720 - 4x \)
2. Add \( 4x \) to both sides:
- \( x + 4x = 720 \)
3. Combine like terms:
- \( 5x = 720 \)
4. Divide by 5:
- \( x = \frac{720}{5} = 144 \)

Finding the Supplement
Now, we can find the supplement of the angle:
- \( 180 - x = 180 - 144 = 36 \)

Conclusion
The angle that is four times its supplement is:
- \( x = 144 \) degrees
- Its supplement is \( 36 \) degrees
This conclusion satisfies the original condition, as \( 144 = 4 \times 36 \).