Question

given parallel lines cut by a transversal, find the value of x

Explanation:

Step1: Set up the equation

When parallel lines are cut by a transversal, alternate - interior angles are equal. So, \(11x - 56=4x + 56\).

Step2: Solve for \(x\)

Subtract \(4x\) from both sides: \(11x-4x - 56=4x-4x + 56\), which simplifies to \(7x-56 = 56\).
Add \(56\) to both sides: \(7x-56 + 56=56 + 56\), so \(7x=112\).
Divide both sides by \(7\): \(x=\frac{112}{7}\).

Answer:

\(x = 16\)