Question

ng lines parallel
parallel lines c and f are cut by transversal b
what is the value of y?

Explanation:

Step1: Use the property of parallel lines

Since lines \(e\) and \(f\) are parallel and cut by transversal \(b\), the angles \((2x + 18)^{\circ}\) and \((4x-14)^{\circ}\) are congruent (corresponding angles). So, \(2x+18 = 4x - 14\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(18=2x - 14\).
Add \(14\) to both sides: \(2x=18 + 14=32\).
Divide by \(2\): \(x = 16\).

Step3: Find the measure of \((4x - 14)^{\circ}\)

Substitute \(x = 16\) into \(4x-14\): \(4\times16-14=64 - 14=50\).

Step4: Use the linear - pair property

The angle \(y^{\circ}\) and \((4x - 14)^{\circ}\) form a linear pair (\(y+(4x - 14)=180\)). Since \(4x - 14 = 50\), then \(y=180-(4x - 14)=180 - 50=130\).

Answer:

\(130\)