Question

1. a civil engineer is designing a road system with two main roads and a cross street. what must the measure of the angle marked x be to ensure that the two main roads are parallel? what relationship is shown? x = __ angle relationship: __

Explanation:

Step1: Recall the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (their sum is \(180^{\circ}\)).

Step2: Set up the equation

If the two main roads are parallel and the given angle is \(52^{\circ}\), then \(x + 52^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(52^{\circ}\) from both sides of the equation: \(x=180^{\circ}- 52^{\circ}\).
\(x = 128^{\circ}\)

Answer:

\(x = 128^{\circ}\), Angle Relationship: Consecutive interior angles (supplementary)