Question

there is a diagram with two parallel lines j and k, and a transversal intersecting them. one angle is (129^circ) and another angle is ((14x - 25)^circ).

Explanation:

Step1: Identify supplementary angles

The angles $(14x - 25)^\circ$ and $129^\circ$ are same-side interior angles formed by a transversal cutting parallel lines, so they are supplementary:
$$(14x - 25) + 129 = 180$$

Step2: Simplify the equation

Combine constant terms:
$$14x + 104 = 180$$

Step3: Isolate the variable term

Subtract 104 from both sides:
$$14x = 180 - 104$$
$$14x = 76$$

Step4: Solve for x

Divide both sides by 14:
$$x = \frac{76}{14} = 11$$

Answer:

$x = 11$