To find the measure of the central angle that cuts an arc of a circular fence with a diameter of 20 feet and an arc length of 4 feet, we can use the formula for the arc length:
\[ L = r \cdot \theta \]
where:
- \( L \) is the arc length,
- \( r \) is the radius of the circle, and
- \( \theta \) is the central angle in radians.
First, we need to calculate the radius \( r \) of the circular fence, which is half of the diameter:
\[ r = \frac{20 \text{ feet}}{2} = 10 \text{ feet} \]
Next, we can rearrange the formula to solve for \( \theta \):
\[ \theta = \frac{L}{r} \]
Substituting the values we have:
\[ \theta = \frac{4 \text{ feet}}{10 \text{ feet}} = 0.4 \text{ radians} \]
To convert radians to degrees, we multiply by \(\frac{180}{\pi}\):
\[ \theta_{\text{degrees}} = 0.4 \cdot \frac{180}{\pi} \approx 22.918 \text{ degrees} \approx 22.9 \text{ degrees} \]
Thus, the measure of the central angle that cuts the arc that measures 4 feet is approximately:
22.9 degrees