Question

given m, 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 \((x - 30)+(3x-10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x-30 + 3x-10=(x + 3x)+(-30-10)=4x-40\). The equation becomes \(4x-40 = 180\).

Step3: Solve for \(x\)

Add \(40\) to both sides of the equation: \(4x-40+40=180 + 40\), which gives \(4x=220\). Then divide both sides by \(4\): \(x=\frac{220}{4}=55\).

Answer:

\(x = 55\)