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

45.8 degrees
45.8 degrees

72 degrees
72 degrees

22.9 degrees
22.9 degrees

226.2 degrees

Answer 1

To find the measure of the central angle that subtends an arc of a circle, we can use the formula:

\[
\text{Central Angle (in degrees)} = \left( \frac{\text{Arc Length}}{\text{Circumference}} \right) \times 360
\]

First, we need to calculate the circumference of the circle. The formula for the circumference \( C \) of a circle is:

\[
C = \pi \times d
\]

where \( d \) is the diameter. Given the diameter is 10 feet:

\[
C = \pi \times 10 \approx 31.42 \text{ feet}
\]

Now, we can calculate the central angle for an arc length of 4 feet:

\[
\text{Central Angle} = \left( \frac{4}{31.42} \right) \times 360
\]

Calculating the fraction:

\[
\frac{4}{31.42} \approx 0.1273
\]

Now, multiply by 360:

\[
\text{Central Angle} \approx 0.1273 \times 360 \approx 45.8 \text{ degrees}
\]

Therefore, the measure of the central angle that cuts the arc that measures 4 feet is **45.8 degrees**.