Question

∠e and ∠f are vertical angles with (mangle e = 5x + 10) and (mangle f = 7x - 12). what is the value of x? enter your answer in the box. (x=square)

Explanation:

Step1: Set up the equation

Since vertical angles are equal, we set $m\angle E=m\angle F$. So, $5x + 10=7x - 12$.

Step2: Move x - terms to one side

Subtract $5x$ from both sides: $5x+10 - 5x=7x - 12-5x$, which simplifies to $10 = 2x-12$.

Step3: Move constant to the other side

Add 12 to both sides: $10 + 12=2x-12 + 12$, resulting in $22 = 2x$.

Step4: Solve for x

Divide both sides by 2: $\frac{22}{2}=\frac{2x}{2}$, so $x = 11$.

Answer:

$11$