Question

(30x + 4)° and 86° formed by intersecting lines (diagram shows intersecting lines with these angles)

Explanation:

Step1: Identify the relationship

The two angles \((30x + 4)^\circ\) and \(86^\circ\) are supplementary (they form a linear pair, so their sum is \(180^\circ\)). So we set up the equation:
\(30x + 4 + 86 = 180\)

Step2: Simplify the equation

Combine like terms:
\(30x + 90 = 180\)

Step3: Solve for \(x\)

Subtract 90 from both sides:
\(30x = 180 - 90\)
\(30x = 90\)

Divide both sides by 30:
\(x = \frac{90}{30}\)
\(x = 3\)

Answer:

\(x = 3\)