To find the central angle that corresponds to an arc length of 4 feet on a circular fence with a diameter of 20 feet, we can use the formula for arc length:
\[ L = r \theta \]
Where \(L\) is the arc length, \(r\) is the radius, and \(\theta\) is the central angle in radians.
First, calculate the radius of the circular fence:
\[ \text{Diameter} = 20 \text{ feet} \implies r = \frac{20}{2} = 10 \text{ feet} \]
Now, using the arc length of 4 feet:
\[ 4 = 10 \theta \]
Now solve for \(\theta\):
\[ \theta = \frac{4}{10} = 0.4 \text{ radians} \]
Next, we need to convert this angle from radians to degrees using the conversion factor \(180^\circ/\pi\):
\[ \theta_{\text{degrees}} = 0.4 \times \frac{180}{\pi} \approx 22.9183 \]
Rounding to one decimal place gives approximately:
\[ \theta_{\text{degrees}} \approx 22.9 \text{ degrees} \]
Thus, the measure of the central angle that cuts the arc measuring 4 feet is:
22.9 degrees.