Question

below are two parallel lines with a third line intersecting them. diagram of two parallel lines cut by a transversal, showing a 116° angle and a z° angle, with x = 64

Explanation:

Step1: Identify angle relationship

The two lines are parallel, and the transversal creates a linear pair with the given \(116^\circ\) angle and angle \(z\). Linear pairs are supplementary, so \(z + 116^\circ = 180^\circ\).

Step2: Solve for \(z\)

Subtract \(116^\circ\) from both sides: \(z = 180^\circ - 116^\circ\).
\(z = 64^\circ\)

Answer:

\(z = 64^\circ\)