Question

in the figure shown below, line m and line n are parallel. what is the value of x?
(figure with parallel lines m and n, a transversal, angles 3x - 10 and 5x + 30, and x = 20 in a box)

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So, \((5x + 30)+(3x-10)=180\).

Step2: Simplify the equation

Combine like - terms: \(5x+3x+30 - 10=180\), which simplifies to \(8x+20 = 180\).

Step3: Solve for \(x\)

Subtract 20 from both sides: \(8x=180 - 20\), so \(8x=160\). Then divide both sides by 8: \(x=\frac{160}{8}\).

Answer:

\(x = 20\)