Question

solve for x.

x =

submit

Explanation:

Step1: Set up the equation

Since \( LM\parallel NO\), the angles \((4x + 54)^{\circ}\) and \((126-2x)^{\circ}\) are same - side interior angles. And same - side interior angles are supplementary (sum to \(180^{\circ}\)). So, \(4x + 54+126-2x=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((4x-2x)+(54 + 126)=180\), which gives \(2x+180 = 180\).

Step3: Solve for \(x\)

Subtract \(180\) from both sides: \(2x+180-180=180 - 180\), so \(2x=0\). Then divide both sides by \(2\): \(x = 0\).

Answer:

\(0\)