Question

∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12.

What is the value of x?

Enter your answer in the box.

x =

Answer 1

To find the value of \( x \), we start with the fact that vertical angles are equal. Therefore, we can set the measures of angles \( E \) and \( F \) equal to each other:

\[
m∠E = m∠F
\]

Substituting the expressions given in the problem:

\[
5x + 10 = 7x - 12
\]

Next, we will solve for \( x \). First, let's move all terms involving \( x \) to one side and constant terms to the other side. We can start by subtracting \( 5x \) from both sides:

\[
10 = 2x - 12
\]

Next, we can add \( 12 \) to both sides to isolate the term with \( x \):

\[
10 + 12 = 2x
\]

\[
22 = 2x
\]

Now, we divide both sides by \( 2 \):

\[
x = \frac{22}{2} = 11
\]

Thus, the value of \( x \) is:

\[
\boxed{11}
\]