Question

which of the following measures is the value of x where lines a and b are parallel?
(6x - 5)° (5x + 10)°
15
45
55
30

Explanation:

Step1: Identify the angle relationship

When two lines are parallel and cut by a transversal, alternate interior angles are equal. Here, \((6x - 5)^\circ\) and \((5x + 10)^\circ\) are alternate interior angles, so they are equal.

$$6x - 5 = 5x + 10$$

Step2: Solve for \(x\)

Subtract \(5x\) from both sides:

$$6x - 5x - 5 = 5x - 5x + 10$$

$$x - 5 = 10$$

Add 5 to both sides:

$$x - 5 + 5 = 10 + 5$$

$$x = 15$$

Answer:

15