use the law of sines. find the measure x to the nearest tenth.

Explanation:

Step1: Apply Law of Sines

$\frac{\sin M}{NR}=\frac{\sin x}{MN}$, substituting $M = 96^{\circ}$, $NR = 15$, $MN=10$ gives $\frac{\sin96^{\circ}}{15}=\frac{\sin x}{10}$.

Step2: Solve for $\sin x$

$\sin x=\frac{10\times\sin96^{\circ}}{15}$.

Step3: Calculate $\sin x$ value

$\sin x=\frac{10\times0.9945}{15}\approx0.663$.

Step4: Find $x$

$x = \sin^{- 1}(0.663)\approx41.5^{\circ}$.

Answer:

$41.5$