Question

find the measures of the labeled angles.
(x + 102)°
4x°
(x + 102)° = 136° (type a whole number.)
4x° = □° (type a whole number.)

Explanation:

Step1: Set up equation

Vertical - angles are equal. So, \(4x=x + 102\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(4x−x=x + 102−x\), which simplifies to \(3x=102\). Then divide both sides by 3: \(x=\frac{102}{3}=34\).

Step3: Find the measure of \(4x\)

Substitute \(x = 34\) into \(4x\). So, \(4x=4\times34 = 136\).

Answer:

\(4x = 136\)