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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![**Problem Statement:**
Given \( m \parallel n \), find the value of \( x \).
**Diagram Explanation:**
The diagram illustrates two parallel lines, \( m \) and \( n \), that are intersected by a transversal line. The angles formed by the transversal and the parallel lines are denoted by algebraic expressions involving \( x \). Specifically, one angle is labeled as \( (6x + 16)^\circ \) and the other is labeled as \( (8x - 18)^\circ \).
**Analysis:**
Since \( m \parallel n \) and these lines are intersected by a transversal, the alternate interior angles are congruent. Therefore, we can set the expressions for the angles equal to each other.
\[ 6x + 16 = 8x - 18 \]
By solving this equation, we can find the value of \( x \).
1. First, subtract \( 6x \) from both sides to get the \( x \) terms on one side:
\[ 16 = 2x - 18 \]
2. Next, add 18 to both sides to isolate the \( x \) term:
\[ 34 = 2x \]
3. Finally, divide both sides by 2 to solve for \( x \):
\[ x = 17 \]
**Conclusion:**
The value of \( x \) is 17.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e193052-f35c-4828-be25-4b465ad72bd4%2F49d67e47-26e7-4e96-866f-f268613e9040%2Fpvvt1m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given \( m \parallel n \), find the value of \( x \).
**Diagram Explanation:**
The diagram illustrates two parallel lines, \( m \) and \( n \), that are intersected by a transversal line. The angles formed by the transversal and the parallel lines are denoted by algebraic expressions involving \( x \). Specifically, one angle is labeled as \( (6x + 16)^\circ \) and the other is labeled as \( (8x - 18)^\circ \).
**Analysis:**
Since \( m \parallel n \) and these lines are intersected by a transversal, the alternate interior angles are congruent. Therefore, we can set the expressions for the angles equal to each other.
\[ 6x + 16 = 8x - 18 \]
By solving this equation, we can find the value of \( x \).
1. First, subtract \( 6x \) from both sides to get the \( x \) terms on one side:
\[ 16 = 2x - 18 \]
2. Next, add 18 to both sides to isolate the \( x \) term:
\[ 34 = 2x \]
3. Finally, divide both sides by 2 to solve for \( x \):
\[ x = 17 \]
**Conclusion:**
The value of \( x \) is 17.
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