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: $$\frac{26}{11}$$