Question

1. your answer

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines are cut by a transversal, the sum of same - side interior angles is \(180^{\circ}\). So, \((x + 78)+(x + 116)=180\).

Step2: Simplify the equation

Combine like terms: \(x+x+78 + 116=180\), which simplifies to \(2x+194 = 180\).

Step3: Solve for \(x\)

Subtract \(194\) from both sides: \(2x=180 - 194=-14\). Then divide both sides by \(2\): \(x=\frac{-14}{2}=-7\).

Answer:

\(x=-7\)