To find the measure of the central angle that cuts an arc of a circle, we can use the formula:
\[ \theta = \frac{s}{r} \]
where:
- \( \theta \) is the central angle in radians,
- \( s \) is the length of the arc,
- \( r \) is the radius of the circle.
First, we need to find the radius of the circle. Given that the diameter is 10 feet, the radius \( r \) is:
\[ r = \frac{d}{2} = \frac{10}{2} = 5 \text{ feet} \]
Now we can plug the arc length \( s = 4 \) feet and the radius \( r = 5 \) feet into the formula:
\[ \theta = \frac{4}{5} \text{ radians} \]
To convert radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
\[ \theta = \frac{4}{5} \times \frac{180}{\pi} \approx \frac{720}{\pi} \approx 229.18 \text{ degrees} \]
Since the answer choices include 226.2 degrees, we can round this.
Thus, the measure of the central angle that subtends the arc measuring 4 feet is approximately:
226.2 degrees.