Question

find the value of the variable and the measure of each labeled angle. (x + 10)° (3x - 34)° x = 22 (type a whole number.) (x + 10)° = □° (type a whole number.)

Explanation:

Step1: Identify vertical angles

The two angles \((x + 10)^\circ\) and \((3x - 34)^\circ\) are vertical angles, so they are equal. Thus, we set up the equation:
\(x + 10 = 3x - 34\)

Step2: Solve for \(x\)

Subtract \(x\) from both sides:
\(10 = 2x - 34\)
Add 34 to both sides:
\(44 = 2x\)
Divide both sides by 2:
\(x = 22\)

Step3: Find the measure of \((x + 10)^\circ\)

Substitute \(x = 22\) into \((x + 10)^\circ\):
\((22 + 10)^\circ = 32^\circ\)

Answer:

\(x = 22\)
\((x + 10)^\circ = 32^\circ\)