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A vertical line is intersected by two parallel lines lower m and lower n forming eight angles.

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

48
48

2611
Start Fraction 26 over 11 End Fraction

10
10

132

1 answer

To solve for \( x \), we can use the fact that angles formed by a transversal intersecting parallel lines have relationships that we can exploit. In this case, angle E and angle B can be considered alternate interior angles.

Given:

  • Angle E = \( 3x + 18 \)
  • Angle B = \( 14x - 8 \)

Since angles E and B are equal (because they are alternate interior angles), we can set up the equation:

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

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

  1. Subtract \( 3x \) from both sides: \[ 18 = 14x - 3x - 8 \] \[ 18 = 11x - 8 \]

  2. Add 8 to both sides: \[ 18 + 8 = 11x \] \[ 26 = 11x \]

  3. Divide both sides by 11: \[ x = \frac{26}{11} \]

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

The correct answer is:

\( \frac{26}{11} \)