Question

1. find x. 4x - 30 x

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, the corresponding angles are equal. Here, \(4x - 30\) and \(x\) are supplementary (because they are same - side interior angles, and for parallel lines, same - side interior angles sum to \(180^{\circ}\)). So, \(4x-30 + x=180\).

Step2: Simplify the equation

Combine like terms: \(5x-30 = 180\).

Step3: Solve for \(x\)

Add \(30\) to both sides: \(5x=180 + 30\), so \(5x=210\).
Divide both sides by \(5\): \(x=\frac{210}{5}\).

Answer:

\(x = 42\)