To find the degree measure of the central angle corresponding to the arc length of a circle, we can use the formula for arc length, which is given by:
\[ L = r \theta \]
where:
- \( L \) is the arc length,
- \( r \) is the radius of the circle, and
- \( \theta \) is the central angle in radians.
We can rearrange this formula to solve for \( \theta \):
\[ \theta = \frac{L}{r} \]
Given:
- \( L = 44 \) inches,
- \( r = 12 \) inches,
we can substitute these values into the equation:
\[ \theta = \frac{44}{12} = \frac{11}{3} \text{ radians} \]
Next, we need to convert radians to degrees. The conversion factor from radians to degrees is:
\[ 180^\circ = \pi \text{ radians} \]
Therefore, to convert \( \theta \) to degrees, we use the conversion:
\[ \theta_{\text{degrees}} = \theta_{\text{radians}} \times \frac{180^\circ}{\pi} \]
Substituting our value of \( \theta \):
\[ \theta_{\text{degrees}} = \frac{11}{3} \times \frac{180^\circ}{\pi} \]
Now we can compute this:
\[ \theta_{\text{degrees}} = \frac{11 \times 180}{3 \pi} = \frac{1980}{3 \pi} \approx \frac{1980}{9.4248} \approx 210.264 \]
Rounding this to the nearest tenth of a degree:
\[ \theta_{\text{degrees}} \approx 210.3^\circ \]
Thus, the degree measure of the central angle is approximately:
\[ \boxed{210.3} \] degrees.
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