I need to find the measure of angle LMN.

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]