Question

lines (ell), (m), and (n) are parallel and cut by transversal (p).

enter the values of (x) and (y).

Explanation:

Step1: Find the value of \(x\)

Since lines \(l\) and \(m\) are parallel and cut by transversal \(p\), the \(108^{\circ}\) angle and \((3x - 6)^{\circ}\) are supplementary (consecutive - interior angles).

$$108+(3x - 6)=180$$

$$3x+102 = 180$$

$$3x=180 - 102$$

$$3x = 78$$

$$x=\frac{78}{3}=26$$

Step2: Find the value of \(y\)

Since lines \(l\) and \(n\) are parallel and cut by transversal \(p\), the \(108^{\circ}\) angle and \((2y)^{\circ}\) are congruent (corresponding angles).

$$2y=108$$

$$y=\frac{108}{2}=54$$

Answer:

\(x = 26\) and \(y = 54\)