Question

find the value of the variable and the measure of each labeled angle.
(x + 25)°
(5x - 27)°
x =
(type a whole number.)

Explanation:

Step1: Identify Vertical Angles

The two angles \((x + 25)^\circ\) and \((5x - 27)^\circ\) are vertical angles, so they are equal.
\[
x + 25 = 5x - 27
\]

Step2: Solve for \(x\)

Subtract \(x\) from both sides:
\[
25 = 4x - 27
\]
Add 27 to both sides:
\[
25 + 27 = 4x
\]
\[
52 = 4x
\]
Divide both sides by 4:
\[
x = \frac{52}{4} = 13
\]

Answer:

\(x = 13\)