Lines m and n are parallel. Angle E measures (3x+18) degrees and angle B measures (14x−8) degrees. What is the value of x?(1 point)Responses 2611 Start Fraction 26 over 11 End Fraction132132101048

Answer 1

Since lines \( m \) and \( n \) are parallel, the angles that are formed when a transversal intersects them are related. In this case, angles \( E \) and \( B \) are alternate interior angles, which means they are equal.

We can set up the equation:

\[ 3x + 18 = 14x - 8 \]

Now, we will solve for \( x \):

1. Subtract \( 3x \) from both sides:

\[ 18 = 14x - 3x - 8 \]

2. Combine like terms:

\[ 18 = 11x - 8 \]

3. Add \( 8 \) to both sides:

\[ 18 + 8 = 11x \]

\[ 26 = 11x \]

4. Divide both sides by \( 11 \):

\[ x = \frac{26}{11} \]

So the value of \( x \) is \( \frac{26}{11} \).