Question

find the measures of the labeled angles. 3x° = □° (type a whole number.)

Explanation:

Step1: Set up the equation

Vertical - angles are equal. So, we set up the equation \(3x=84 - x\).

Step2: Add \(x\) to both sides

To get all \(x\) - terms on one side, we add \(x\) to both sides of the equation: \(3x+x=84 - x+x\), which simplifies to \(4x = 84\).

Step3: Solve for \(x\)

Divide both sides of the equation \(4x = 84\) by 4: \(x=\frac{84}{4}=21\).

Step4: Find the measure of \(3x\)

Substitute \(x = 21\) into \(3x\). So, \(3x=3\times21 = 63\).

Answer:

63