Question

two parallel lines, a and b, are cut by transversal w. the measures of two angles formed are given. what is the measurement of the angle labeled (3x)° if ∠y = 60°?

Explanation:

Step1: Identify angle - relationship

When two parallel lines are cut by a transversal, corresponding angles are equal. The angle labeled \((3x)^{\circ}\) and \(\angle Y\) are corresponding angles. So \(3x=\angle Y\).

Step2: Substitute the value of \(\angle Y\)

Given \(\angle Y = 60^{\circ}\), we have the equation \(3x=60\).

Step3: Solve for \(x\)

Divide both sides of the equation \(3x = 60\) by 3: \(x=\frac{60}{3}=20\). Then the measure of the angle \((3x)^{\circ}\) is \(3\times20 = 60^{\circ}\).

Answer:

\(60^{\circ}\)