Question

below are two parallel lines with a third line intersecting them.
x = \square ^\circ

Explanation:

Step1: Identify angle relationship

The two lines are parallel, and the transversal creates same - side interior angles (or we can also consider the concept of supplementary angles for parallel lines cut by a transversal). The given angle is \(116^{\circ}\), and the angle \(x\) and the \(116^{\circ}\) angle are supplementary (they form a linear pair or are same - side interior angles which are supplementary when lines are parallel).
The formula for supplementary angles is \(a + b=180^{\circ}\), where \(a = 116^{\circ}\) and \(b=x\).

Step2: Solve for \(x\)

Using the supplementary angle formula \(x + 116^{\circ}=180^{\circ}\).
Subtract \(116^{\circ}\) from both sides: \(x=180^{\circ}- 116^{\circ}\).
Calculate \(180 - 116 = 64\), so \(x = 64^{\circ}\).

Answer:

\(64\)