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, \((10x - 10)+(5x + 10)=180\).

Step2: Simplify the equation

Combine like - terms: \(10x-10 + 5x+10=180\), which simplifies to \(15x=180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(15x = 180\) by \(15\): \(x=\frac{180}{15}\).

Answer:

\(x = 12\)