Question

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, \((10x + 8)+(7x+2)=180\).

Step2: Simplify the equation

Combine like - terms: \(10x+7x+8 + 2=180\), which gives \(17x+10 = 180\).

Step3: Solve for \(x\)

Subtract \(10\) from both sides: \(17x=180 - 10=170\). Then divide both sides by \(17\): \(x=\frac{170}{17}=10\).

Answer:

\(x = 10\)