#### Answer

$x \approx 17.5$

#### Work Step by Step

In this exercise, we are given the measure of a non-included side and two angles. We can use the law of sines to find the measure of another line in the triangle. The law of sines states the following:
$\frac{sin A}{a}$ = $\frac{sin X}{x}$
Let's plug in what we know into the formula:
$\frac{sin 40}{12}$ = $\frac{sin 110}{x}$
Multiply each side by $x$:
$\frac{sin 40}{12}(x)$ = sin $110$
Divide both sides by $\frac{sin 40}{12}$ to solve for $x$:
$x \approx 17.5$