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, the consecutive - interior angles are supplementary. So, \((2x - 29)+(10x + 5)=180\).

Step2: Simplify the equation

Combine like terms: \(2x+10x-29 + 5=180\), which gives \(12x-24 = 180\).

Step3: Solve for \(x\)

Add \(24\) to both sides of the equation: \(12x=180 + 24\), so \(12x=204\). Then divide both sides by \(12\): \(x=\frac{204}{12}=18\).

Answer:

\(x = 18\)