<u>Given</u>:
Given that two lines are intersecting at the point.
The angles (3x - 8)° and (2x + 12)° are the angles formed by the intersection of the two lines.
We need to determine the equation to solve for x and the value of x.
<u>Equation:</u>
The two angles (3x - 8)° and (2x + 12)° are vertically opposite. Hence, the vertically opposite angles are always equal.
Hence, we have;
Hence, the equation is
<u>Value of x:</u>
The value of x can be determined by solving the equation
Thus, we have;
Subtracting both sides of the equation by 2x, we get;
Adding both sides of the equation by 8, we get;
Thus, the value of x is 20.
Hence, the equation and the value of x are
Thus, Option D is the correct answer.