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Arc XY located on circle A has a length of 40 centimeters. The radius of the circle is 10 centimeters. What is the measure of the corresponding central angle for ∠XY in radians?

A. [tex]\(\frac{3}{4} \pi\)[/tex]

B. 3

C. [tex]\(\frac{4}{3} \pi\)[/tex]

D. 4

Sagot :

GinnyAnswer
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
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