Question

find the measures of the labeled angles.
3x° = 63° (type a whole number.)
(84 - x)° = □° (type a whole number.)

Explanation:

Step1: Set up equation

Vertical - angles are equal. So, \(3x=84 - x\).

Step2: Add \(x\) to both sides

\(3x+x=84 - x+x\), which simplifies to \(4x = 84\).

Step3: Solve for \(x\)

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

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

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

Step5: Find the measure of \(84 - x\)

Substitute \(x = 21\) into \(84 - x\), so \(84 - 21=63\).

Answer:

\(3x = 63\), \((84 - x)=63\)