Question

two parallel lines are crossed by a transversal. what is the value of y? y = 30, y = 50, y = 110, y = 130

Explanation:

Step1: Identify angle relationship

The two parallel lines \(b\) and \(c\) are cut by transversal \(a\). The \(50^\circ\) angle and \(y^\circ\) angle are same - side interior angles. For two parallel lines cut by a transversal, same - side interior angles are supplementary, which means their sum is \(180^\circ\).

Step2: Solve for \(y\)

We know that if two angles are supplementary, then \(50 + y=180\). To find \(y\), we subtract \(50\) from both sides of the equation: \(y = 180 - 50\).
\(y=130\)

Answer:

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