Question

given ( mparallel n ), find the value of x.

Explanation:

Step1: Use the property of parallel lines

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), the consecutive interior angles are supplementary. So, \((4x - 8)+(7x-20)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x+7x-8 - 20=180\), which gives \(11x-28 = 180\).

Step3: Solve for \(x\)

Add \(28\) to both sides of the equation: \(11x-28 + 28=180 + 28\), so \(11x=208\). Then divide both sides by \(11\): \(x=\frac{208}{11}\approx18.91\). Wait, no, made a mistake. Wait, actually, if they are alternate - interior angles (assuming the figure is such that they are equal, since the problem might have a mis - description in the initial thought. Let's re - check. If they are alternate - interior angles (a common case for parallel lines cut by a transversal), then \(4x-8=7x - 20\).

Step3 (corrected): Solve the correct equation

Subtract \(4x\) from both sides: \(-8 = 3x-20\). Then add \(20\) to both sides: \(12 = 3x\). Divide both sides by \(3\): \(x = 4\).

Answer:

\(x = 4\)