Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![### Determine the Value of x to Ensure Parallel Lines
**Problem Statement:**
Find the value of \( x \) that makes lines \( u \) and \( v \) parallel.
**Given Diagram:**
The diagram features two horizontal lines labeled \( u \) and \( v \) that are cut by a transversal. There is an angle of \( 80^\circ \) on the upper section between line \( u \) and the transversal. The corresponding angle on the lower section between line \( v \) and the transversal is labeled \( x + 104 \).
1. The diagram looks as follows (with lines \( u \) and \( v \) being parallel if corresponding angles are equal):
```
u
⎯⎯⎯⎯⎯⎯⎯
\
\ 80°
\
⎯⎯⎯⎯⎯⎯⎯
v x + 104
```
**Options for the value of \( x \):**
A) \(-9\)
B) \(-4\)
C) \(5\)
D) \(4\)
**Solution Explanation:**
To make lines \( u \) and \( v \) parallel, the corresponding angles formed by the transversal must be equal. Therefore, we set up the following equation:
\[ 80^\circ = x + 104^\circ \]
Solving for \( x \):
\[ 80 = x + 104 \]
\[ x = 80 - 104 \]
\[ x = -24 \]
However, looking at the given options, \(-24\) is not listed. This indicates an error either in the transcription of the problem or in the potential answer choices provided.
Therefore, we conclude that none of the given options (A, B, C, D) are correct and there may be additional context or a revision of options needed to correctly answer this educational problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcd2ce70f-8083-47d5-80fb-9f8903ac6d5a%2Fba63a9e0-59e5-43f3-ac6d-c79301be9d4c%2Ftybone_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Determine the Value of x to Ensure Parallel Lines
**Problem Statement:**
Find the value of \( x \) that makes lines \( u \) and \( v \) parallel.
**Given Diagram:**
The diagram features two horizontal lines labeled \( u \) and \( v \) that are cut by a transversal. There is an angle of \( 80^\circ \) on the upper section between line \( u \) and the transversal. The corresponding angle on the lower section between line \( v \) and the transversal is labeled \( x + 104 \).
1. The diagram looks as follows (with lines \( u \) and \( v \) being parallel if corresponding angles are equal):
```
u
⎯⎯⎯⎯⎯⎯⎯
\
\ 80°
\
⎯⎯⎯⎯⎯⎯⎯
v x + 104
```
**Options for the value of \( x \):**
A) \(-9\)
B) \(-4\)
C) \(5\)
D) \(4\)
**Solution Explanation:**
To make lines \( u \) and \( v \) parallel, the corresponding angles formed by the transversal must be equal. Therefore, we set up the following equation:
\[ 80^\circ = x + 104^\circ \]
Solving for \( x \):
\[ 80 = x + 104 \]
\[ x = 80 - 104 \]
\[ x = -24 \]
However, looking at the given options, \(-24\) is not listed. This indicates an error either in the transcription of the problem or in the potential answer choices provided.
Therefore, we conclude that none of the given options (A, B, C, D) are correct and there may be additional context or a revision of options needed to correctly answer this educational problem.
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