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 sum of the interior angles on the same side of the transversal is \(180^{\circ}\). So, \((8x - 5)+(x + 5)=180\).

Step2: Simplify the equation

Combine like - terms: \(8x-5+x + 5=180\). The \(-5\) and \(+5\) cancel out, and we get \(9x=180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(9x = 180\) by \(9\). So, \(x=\frac{180}{9}=20\).

Answer:

\(20\)