Question

find the measures of the labeled angles. (x + 120)° 6x° (x + 120)° = □° (type a whole number.)

Explanation:

Step1: Set up the equation

Vertical - angles are equal. So, \(x + 120=5x\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(120 = 5x−x\), which simplifies to \(120 = 4x\). Then divide both sides by 4: \(x=\frac{120}{4}=30\).

Step3: Find the measure of the angle \((x + 120)^{\circ}\)

Substitute \(x = 30\) into \(x + 120\). We get \(30+120 = 150\).

Answer:

150