Question

two parallel lines are crossed by a transversal. what is the value of y? options: y = 30, y = 50, y = 110, y = 130 (with a diagram of two parallel lines b and c crossed by transversal a, showing a 50° angle and y° angle)

Explanation:

Step1: Identify angle relationship

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^\circ\)). The \(50^\circ\) angle and \(y^\circ\) are consecutive interior angles.

Step2: Set up the equation

Using the supplementary angle relationship: \(y + 50 = 180\)

Step3: Solve for y

Subtract 50 from both sides: \(y = 180 - 50 = 130\)

Answer:

\(y = 130\) (corresponding to the option \(y = 130\))