Question

given ( mparallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of parallel lines

When \(m\parallel n\), the angles \((10x + 8)^{\circ}\) and \((7x+2)^{\circ}\) are supplementary. 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 \(17\): \(x=\frac{170}{17}=14\).

Answer:

\(x = 14\)