To find the measure of the central angle for the arc [tex]\( \widehat{XY} \)[/tex] in radians, we can use the relationship between the arc length, the radius of the circle, and the central angle in radians. The formula to find the central angle [tex]\( \theta \)[/tex] in radians is given by:
[tex]\[
\theta = \frac{\text{arc length}}{\text{radius}}
\][/tex]
Given:
- Arc length = 40 centimeters
- Radius = 10 centimeters
Substitute the given values into the formula:
[tex]\[
\theta = \frac{40 \text{ cm}}{10 \text{ cm}}
\][/tex]
Simplify the expression:
[tex]\[
\theta = 4 \text{ radians}
\][/tex]
Thus, the measure of the central angle corresponding to [tex]\( \widehat{XY} \)[/tex] is 4 radians.
Therefore, the correct answer is:
D. 4
