Question

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

10
10

132
132

48
48

2611

Answer 1

Line segment AC¯¯¯¯¯¯¯¯
is a perpendicular bisector of segment BD¯¯¯¯¯¯¯¯
, with the two segments meeting at point E
. What is true of segment BE¯¯¯¯¯¯¯¯
? (1 point)
Responses

It must be the same length as segment EA¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper C upper D .

It must be the same length as segment DE¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper D upper E .

It must be the same length as segment BC¯¯¯¯¯¯¯¯
.
It must be the same length as segment upper B upper C .

It must be the same length as segment AB¯¯¯¯¯¯¯¯
.

Answer 2

When two lines are parallel, certain angles are equal or supplementary depending on their position relative to each other (e.g., corresponding angles, alternate interior angles, etc.). To find the value of \( x \) in your problem, we need to identify which angles are equal.

Since lines \( m \) and \( n \) are parallel, angle \( E \) and angle \( B \) are likely either corresponding angles or alternate interior angles, which means they are equal.

Set the two angle expressions equal to each other:

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

Now, 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:
\[
x = \frac{26}{11}
\]

Since this value is approximately \( 2.36 \) and not fitting any of the provided multiple-choice options (10, 132, 48, 2611), it's possible there might be an error in the definitions of angles or their relations, or a misinterpretation of their equations. If both angles were to be supplementary, you would set:

\[
3x + 18 + 14x - 8 = 180
\]

Calculating this would give:

\[
17x + 10 = 180
\]
\[
17x = 170
\]
\[
x = 10
\]

Given that value, if indeed angle E and angle B are supplementary, \( x = 10 \) becomes the relevant solution. Thus, the answer you should select is:

**10**.