Question

Question

Use the image to answer the question.

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

132
132

10
10

2611
Start Fraction 26 over 11 End Fraction

48
48
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Answer 1

To find the value of \( x \), we can use the fact that angle \( E \) and angle \( B \) are corresponding angles formed when a transversal (the vertical line) intersects the two parallel lines (lines \( m \) and \( n \)). Since corresponding angles are congruent, we can set the measures of the two angles equal to each other:

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

Now, let's solve for \( x \).

1. Rearranging the equation: \[ 3x + 18 + 8 = 14x \] \[ 26 = 14x - 3x \] \[ 26 = 11x \]

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

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

Thus, the answer is: \[ \frac{26}{11} \]