Question

∠e and ∠f are vertical angles with ( mangle e = 9x + 12 ) and ( mangle f = 3x + 24 ). what is the value of x? enter your answer in the box. ( x = )

Explanation:

Step1: Set up the equation

Since vertical angles are equal, \(9x + 12=3x + 24\).

Step2: Subtract \(3x\) from both sides

\(9x-3x + 12=3x-3x + 24\), which simplifies to \(6x+12 = 24\).

Step3: Subtract \(12\) from both sides

\(6x+12 - 12=24 - 12\), resulting in \(6x=12\).

Step4: Divide both sides by \(6\)

\(\frac{6x}{6}=\frac{12}{6}\), so \(x = 2\).

Answer:

\(2\)