Question

parallel lines e and f are cut by transversal b. what is the value of y? (2x + 18)° (4x - 14)° y° options: 16, 50, 130, 164

Explanation:

Step1: Identify Angle Relationship

Since lines \( e \) and \( f \) are parallel and cut by transversal \( b \), the angles \( (2x + 18)^\circ \) and \( (4x - 14)^\circ \) are alternate exterior angles (or corresponding, depending on position), so they are equal.
Set \( 2x + 18 = 4x - 14 \).

Step2: Solve for \( x \)

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

Step3: Find \( (4x - 14)^\circ \)

Substitute \( x = 16 \): \( 4(16) - 14 = 64 - 14 = 50^\circ \).

Step4: Find \( y \)

The angle \( y^\circ \) and \( (4x - 14)^\circ \) are supplementary (linear pair), so \( y + 50 = 180 \).
Subtract 50: \( y = 130 \).

Answer:

130