Question

what is the value of x?

Explanation:

Step1: Identify angle - pair relationship

Assume the two parallel lines are cut by a transversal. Angle 74° and the angle with measure \(6x + 2\) are corresponding angles (or alternate - exterior/alternate - interior depending on the parallel - line properties). Corresponding angles (or alternate - exterior/alternate - interior angles when lines are parallel) are equal. So, \(6x+2 = 74\).

Step2: Solve the equation for \(x\)

Subtract 2 from both sides of the equation \(6x+2 = 74\). We get \(6x=74 - 2\), so \(6x=72\). Then divide both sides by 6: \(x=\frac{72}{6}\).

Answer:

12