To find the measure of the central angle in radians for an arc on a circle, we can use the relationship between the arc length, the radius of the circle, and the central angle. The formula for the central angle [tex]\(\theta\)[/tex] (in radians) is given by:
[tex]\[
\theta = \frac{\text{arc length}}{\text{radius}}
\][/tex]
Given:
- The arc length [tex]\( = 40 \)[/tex] centimeters
- The radius [tex]\( = 10 \)[/tex] centimeters
Substituting the given values into the formula, we get:
[tex]\[
\theta = \frac{40}{10} = 4
\][/tex]
Thus, the measure of the corresponding central angle for [tex]\(\hat{XY}\)[/tex] in radians is [tex]\(4\)[/tex].
The correct answer is:
D. 4
