Question

skill set #3 5 - angle relationships with parallel lines
given ( mparallel n ), find the value of x.

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines \(m\parallel n\) are cut by a transversal \(t\), consecutive interior angles are supplementary. So \((4x + 8)+(2x+10)=180\).

Step2: Simplify the equation

Combine like - terms: \(4x+2x+8 + 10=180\), which gives \(6x+18 = 180\).

Step3: Solve for \(x\)

Subtract 18 from both sides: \(6x=180 - 18\), so \(6x=162\). Then divide both sides by 6: \(x=\frac{162}{6}=27\).

Answer:

\(x = 27\)