Question

given the following, what is the value of x? image of two parallel vertical lines and a transversal with angle expressions 7x + 9 and 6x + 15 select the correct answer options: 0, 6, 15, 1.5

Explanation:

Step1: Identify the relationship

The two angles \(7x + 9\) and \(6x + 27\) are alternate interior angles (since the lines are parallel, alternate interior angles are equal). So we set up the equation: \(7x + 9 = 6x + 27\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(7x - 6x + 9 = 6x - 6x + 27\), which simplifies to \(x + 9 = 27\). Then subtract 9 from both sides: \(x + 9 - 9 = 27 - 9\), so \(x = 18\).

Answer:

18