Answer:
76°
Step-by-step explanation:
To find the measure of arc NL, we can use the Inscribed Angle Theorem.
According to the Inscribed Angle Theorem, the measure of an inscribed angle is equal to half the measure of its intercepted arc, so the intercepted arc is twice the measure of the inscribed angle.
In this case, the inscribed angle is ∠NML and the intercepted arc is arc NL. Therefore:
[tex]\begin{aligned}\overset\frown{NL}&=2 \cdot m\angle NML\\\\\overset\frown{NL}&=2 \cdot 38^{\circ}\\\\\overset\frown{NL}&=76^{\circ}\end{aligned}[/tex]
Therefore, the measure of arc NL is 76°.
