Question

solve for x.

Explanation:

Step1: Identify angle - relationship

Assume the two horizontal lines are parallel. The angle \(5x + 30^{\circ}\) and the \(45^{\circ}\) angle are corresponding angles (or alternate - exterior angles depending on the parallel - line properties). When two parallel lines are cut by a transversal, corresponding angles (or alternate - exterior angles) are equal.
So, we set up the equation \(5x+30 = 45\).

Step2: Solve the equation for \(x\)

Subtract 30 from both sides of the equation: \(5x=45 - 30\).
\(5x=15\).
Then divide both sides by 5: \(x=\frac{15}{5}\).

Answer:

\(x = 3\)