Question

1. in the figure shown below, lines a and b are paral and line c is a transversal. what is the value of x? a. 6 b. 9 c. 12 d. 18

Explanation:

Step1: Use the property of alternate interior angles

Since lines \(a\) and \(b\) are parallel and \(c\) is a transversal, the alternate interior angles are equal. So, \(13x + 6=11x + 30\).

Step2: Solve the equation for \(x\)

Subtract \(11x\) from both sides: \(13x-11x + 6=11x-11x + 30\), which simplifies to \(2x+6 = 30\).
Subtract \(6\) from both sides: \(2x+6 - 6=30 - 6\), getting \(2x=24\).
Divide both sides by \(2\): \(x=\frac{24}{2}=12\).

Answer:

C. 12