Respuesta :

notice the circle, the radius NM or ML is 5, and the arc the angle makes is 14.3 cm, thus

[tex]\bf \textit{arc's legnth}\\\\ s=\cfrac{\pi \theta r}{180}\quad \begin{cases} r=5\\ s=14.3\\ \theta =angle~in\\ \qquad degrees \end{cases}\implies 14.3=\cfrac{\pi \theta 5}{180}\implies \cfrac{14.3\cdot 180}{5\pi }=\theta [/tex]
akposevictor

The measure of the angle LMN in the circle with the given arc length is approximately: 164°

How to Find the Length of an Arc?

The formula for arc length of a circle is, s = ∅/360 × 2πr, where r is the radius and ∅ is the central angle measure.

Given the following:

  • Arc length (s) = 14.3 cm
  • Radius (r) = 5 cm

Plug in the values into the formula:

14.3 = ∅/360 × 2π(5)

14.3 = ∅/360 × 31.4

(360)(14.3) = (∅)(31.4)

5,148 = (∅)(31.4)

∅ = 5,148/31.4

∅ = 5,148/31.4

∅ ≈ 164°

Learn more about arc length on:

https://brainly.com/question/2005046

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