To determine the measure of the central angle corresponding to the arc, we can use the relationship between the arc length, the radius of the circle, and the central angle in radians.
The formula for the central angle [tex]\(\theta\)[/tex] in radians is given by:
[tex]\[
\theta = \frac{\text{arc length}}{\text{radius}}
\][/tex]
We are given:
- The arc length is 40 centimeters.
- The radius of the circle is 10 centimeters.
Substituting these values into the formula, we get:
[tex]\[
\theta = \frac{40 \, \text{cm}}{10 \, \text{cm}} = 4 \, \text{radians}
\][/tex]
Thus, the measure of the corresponding central angle for [tex]\(\widehat{XY}\)[/tex] is 4 radians.
Therefore, the correct answer is:
B. 4
