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Step1: Use the property of consecutive interior angles
When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So, \((2x + 9)+43 = 180\).
Step2: Simplify the equation
\(2x+9 + 43=180\) simplifies to \(2x+52 = 180\).
Step3: Solve for \(x\)
Subtract \(52\) from both sides: \(2x=180 - 52\), so \(2x = 128\). Then divide both sides by \(2\): \(x=\frac{128}{2}\).
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\(x = 64\)