Question

solve for x.

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So, \((6x + 32)+(72 - 2x)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((6x-2x)+(32 + 72)=180\), which gives \(4x+104 = 180\).

Step3: Solve for \(x\)

Subtract 104 from both sides: \(4x=180 - 104\), so \(4x=76\). Then divide both sides by 4: \(x=\frac{76}{4}\).

Answer:

\(x = 19\)