Question

question
in circle k, kl = 15 and the length of \\(\overarc{lm} = 5\pi\\). find \\(m\angle lkm\\).
answer attempt 1 out of 3
\\(m\angle lkm = \square ^\circ\\) submit answer

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{n\pi r}{180}\), where \(n\) is the central angle in degrees and \(r\) is the radius of the circle.
Given \(s = 5\pi\) and \(r=KL = 15\).

Step2: Substitute the values into the formula

Substitute \(s = 5\pi\) and \(r = 15\) into \(s=\frac{n\pi r}{180}\).
We get \(5\pi=\frac{n\pi\times15}{180}\).
First, cancel out \(\pi\) from both sides of the equation. The equation becomes \(5=\frac{15n}{180}\).

Step3: Solve for \(n\)

Cross - multiply: \(15n=5\times180\).
\(15n = 900\).
Divide both sides by 15: \(n=\frac{900}{15}=60\).

Answer:

\(60\)