Question

12, x, (12x - 5)°, 85°, y, z, w, m ∠xyz = 128°

Explanation:

Step1: Set up the angle equation

The measure of $\angle XYZ$ is the sum of the measure of $\angle XYW$ (which is $(12x - 5)^\circ$) and the measure of $\angle WYZ$ (which is $85^\circ$). So we have the equation:
$$(12x - 5) + 85 = 128$$

Step2: Simplify the left - hand side

First, combine like terms on the left - hand side of the equation. $-5 + 85 = 80$, so the equation becomes:
$$12x+80 = 128$$

Step3: Solve for x

Subtract 80 from both sides of the equation:
$$12x=128 - 80$$
$$12x = 48$$
Then divide both sides by 12:
$$x=\frac{48}{12}$$
$$x = 4$$

Answer:

$x = 4$