Question

If a circle has a 10 foot diameter, then what is the measure of the central angle that cuts the arc that measures 4 feet?(1 point)
Responses

226.2 degrees
226.2 degrees

72 degrees
72 degrees

22.9 degrees
22.9 degrees

45.8 degrees

Answer 1

To find the measure of the central angle corresponding to an arc length, you can use the formula:

\[
\theta = \frac{s}{r}
\]

where \( \theta \) is the central angle in radians, \( s \) is the arc length, and \( r \) is the radius of the circle.

1. **Find the radius**: The diameter of the circle is 10 feet, so the radius \( r \) is half of that:
\[
r = \frac{10}{2} = 5 \text{ feet}
\]

2. **Use the arc length**: The arc length \( s \) is given as 4 feet.

3. **Calculate the central angle in radians**:
\[
\theta = \frac{s}{r} = \frac{4}{5} = 0.8 \text{ radians}
\]

4. **Convert radians to degrees**: To convert radians to degrees, you can use the conversion factor \( \frac{180}{\pi} \):
\[
\theta \text{ (degrees)} = 0.8 \times \frac{180}{\pi} \approx 45.835 \text{ degrees}
\]

Rounding to one decimal place gives approximately \( 45.8 \) degrees.

So, the measure of the central angle that cuts the arc that measures 4 feet is:

**45.8 degrees**.