Question

for questions 17 - 18, find the value of x that would prove j || k.
state the converse that justifies your answer.
18.

Explanation:

Step1: Identify the relationship between angles

When \(j\parallel k\), the angles \((14x - 25)^{\circ}\) and \(129^{\circ}\) are same - side interior angles. By the converse of the same - side interior angles theorem, if two lines are cut by a transversal and the same - side interior angles are supplementary, then the lines are parallel. So, \((14x-25)+129 = 180\).

Step2: Solve the equation

$$
LATEXBLOCK0
$$

For problem 18:

Step1: Identify the relationship between angles

When \(j\parallel k\), the angles \((2x - 8)^{\circ}\) and \((9x-10)^{\circ}\) are consecutive interior angles. By the converse of the consecutive interior angles theorem (same - side interior angles theorem), if two lines are cut by a transversal and the same - side interior angles are supplementary, then the lines are parallel. So, \((2x - 8)+(9x-10)=180\).

Step2: Solve the equation

$$
LATEXBLOCK1
$$

Answer:

For the first problem (assuming it's problem 17 in the original set where the angles are \((14x - 25)^{\circ}\) and \(129^{\circ}\)), \(x = \frac{38}{7}\) by the converse of the same - side interior angles theorem. For problem 18, \(x = 18\) by the converse of the same - side interior angles theorem.