What value of x would prove a||b? a. x = 6.9 12x+3 b. x = 6 C. x = 12 d. x = 4.2 21x-51,

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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**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:** \( x = 6 \)
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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