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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Question
![**Parallel Lines and Angles - Educational Explanation**
**Question:** What value of \( x \) would prove \( a \parallel b \)?
**Diagram Description:**
- There are two horizontal lines labeled as \( a \) and \( b \).
- A transversal intersects lines \( a \) and \( b \).
- The angle formed between the transversal and line \( a \) is expressed as \( 12x + 3 \).
- The angle formed between the transversal and line \( b \) is expressed as \( 21x - 51 \).
**Options:**
a. \( x = 6.9 \)
b. \( x = 6 \)
c. \( x = 12 \)
d. \( x = 4.2 \)
For the lines \( a \) and \( b \) to be parallel, the corresponding angles need to be equal. Therefore, set the expressions equal to each other and solve for \( x \):
\[ 12x + 3 = 21x - 51 \]
Subtract \( 12x \) from both sides:
\[ 3 = 9x - 51 \]
Add 51 to both sides:
\[ 54 = 9x \]
Divide by 9:
\[ x = 6 \]
Therefore, the correct value of \( x \) that proves \( a \parallel b \) is found in option b:
**Answer:** \( x = 6 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febcd91cf-c92a-4a76-9c9a-e8d21c0f504d%2F6cd56095-8c10-421f-948b-f2ca35863850%2Fidiulc4i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Parallel Lines and Angles - Educational Explanation**
**Question:** What value of \( x \) would prove \( a \parallel b \)?
**Diagram Description:**
- There are two horizontal lines labeled as \( a \) and \( b \).
- A transversal intersects lines \( a \) and \( b \).
- The angle formed between the transversal and line \( a \) is expressed as \( 12x + 3 \).
- The angle formed between the transversal and line \( b \) is expressed as \( 21x - 51 \).
**Options:**
a. \( x = 6.9 \)
b. \( x = 6 \)
c. \( x = 12 \)
d. \( x = 4.2 \)
For the lines \( a \) and \( b \) to be parallel, the corresponding angles need to be equal. Therefore, set the expressions equal to each other and solve for \( x \):
\[ 12x + 3 = 21x - 51 \]
Subtract \( 12x \) from both sides:
\[ 3 = 9x - 51 \]
Add 51 to both sides:
\[ 54 = 9x \]
Divide by 9:
\[ x = 6 \]
Therefore, the correct value of \( x \) that proves \( a \parallel b \) is found in option b:
**Answer:** \( x = 6 \)
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