Question

∠e and ∠f are vertical angles with ( mangle e = 8x + 8 ) and ( mangle f = 2x + 38 ). what is the value of x? enter your answer in the box. ( x = )

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(m\angle E=m\angle F\).
This gives the equation \(8x + 8=2x+38\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides:
\(8x-2x + 8=2x-2x+38\)
\(6x + 8=38\)
Subtract \(8\) from both sides:
\(6x+8 - 8=38 - 8\)
\(6x=30\)
Divide both sides by \(6\):
\(x=\frac{30}{6}=5\)

Answer:

\(x = 5\)