Question

two parallel lines are cut by a transversal. ∠1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle with ∠1 measures (14x + 8)°. what is the value of x?

Explanation:

Step1: Use the property of adjacent angles

When two parallel lines are cut by a transversal, \(\angle1\) and its adjacent angle (which is \((14x + 8)^{\circ}\)) are supplementary. So, \((4x+28)+(14x + 8)=180\).

Step2: Simplify the equation

Combine like - terms: \(4x+14x+28 + 8=180\), which gives \(18x+36 = 180\).

Step3: Solve for \(x\)

Subtract 36 from both sides: \(18x=180 - 36=144\). Then divide both sides by 18: \(x=\frac{144}{18}=8\).

Answer:

\(8\)