Question

find ( mangle n ).

( mangle n = square^circ )

Explanation:

Step1: Identify the major arc

The arc opposite to $\angle N$ is the labeled $160^\circ$ arc, so the remaining arc $\overset{\frown}{LM}$ is calculated as:
$$360^\circ - 160^\circ = 200^\circ$$

Step2: Apply inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. $\angle N$ intercepts $\overset{\frown}{LM}$, so:
$$m\angle N = \frac{1}{2} \times 200^\circ$$

Answer:

$100$