Question

find the value of the variable.
x = □ (simplify your answer)

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Here, the angle measuring $6x$ and the angle measuring $(96 - x)$ are vertical angles. So, we set up the equation $6x=96 - x$.

Step2: Solve the equation for $x$

Add $x$ to both sides of the equation: $6x+x=96 - x+x$, which simplifies to $7x = 96$. Then divide both sides by 7: $x=\frac{96}{7}$.

Answer:

$\frac{96}{7}$