To find the measure of the central angle corresponding to an arc on a circle, we use the relationship between the arc length, radius, and central angle. This relationship is given by 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,
- [tex]\( r \)[/tex] is the radius of the circle.
Given:
- The length of arc [tex]\( XY \)[/tex] (s) is 40 centimeters,
- The radius of the circle (r) is 10 centimeters.
Substitute the known values into the formula:
[tex]\[ \theta = \frac{40 \, \text{cm}}{10 \, \text{cm}} \][/tex]
Simplify the fraction:
[tex]\[ \theta = 4 \, \text{radians} \][/tex]
Therefore, the measure of the central angle for arc [tex]\( XY \)[/tex] is 4 radians.
The correct answer is:
A. 4
