Question

solve for x.

Explanation:

Step1: Identify angle - relationship

Assume the two vertical - lines are parallel. The angles \((59 - 5x)^{\circ}\) and \((53 - 2x)^{\circ}\) are corresponding angles. For parallel lines, corresponding angles are equal.
So we set up the equation \(59−5x = 53−2x\).

Step2: Solve the equation for \(x\)

First, add \(5x\) to both sides of the equation:
\(59=53 - 2x+5x\), which simplifies to \(59 = 53+3x\).
Then subtract 53 from both sides: \(59 - 53=3x\), so \(6 = 3x\).
Finally, divide both sides by 3: \(x=\frac{6}{3}=2\).

Answer:

\(2\)