Certainly! Let's break down the solution step by step.
1. To find the measure of the central angle corresponding to an arc on a circle, we can use the formula:
[tex]\[
\theta = \frac{s}{r}
\][/tex]
where [tex]\(\theta\)[/tex] is the measure of the central angle in radians, [tex]\(s\)[/tex] is the arc length, and [tex]\(r\)[/tex] is the radius of the circle.
2. We are given the following information:
- The arc length ([tex]\(s\)[/tex]) is 40 centimeters.
- The radius ([tex]\(r\)[/tex]) is 10 centimeters.
3. Plugging these values into the formula, we get:
[tex]\[
\theta = \frac{40}{10}
\][/tex]
4. Simplifying the fraction, we find:
[tex]\[
\theta = 4
\][/tex]
Therefore, the measure of the corresponding central angle for arc XY in radians is [tex]\(4\)[/tex].
From the given options:
A. [tex]\(\frac{3}{4} \pi\)[/tex]
B. 4
C. 3
D. [tex]\(\frac{4}{3} \pi\)[/tex]
The correct answer is:
B. 4
