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 consists of two parallel lines labeled \( m \) and \( n \). A transversal line intersects these two parallel lines, creating several angles.
- On the upper parallel line \( m \), one of the angles formed by the transversal is labeled \( (7x - 4)^\circ \).
- On the lower parallel line \( n \), the corresponding angle formed by the transversal is labeled \( (5x + 10)^\circ \).
Since \( m \parallel n \) and the transversal intersects both lines, these corresponding angles are congruent, meaning they are equal to each other.
### Setup the Equation
Since corresponding angles are equal, we set the angles equal to each other:
\[ (7x - 4)^\circ = (5x + 10)^\circ \]
### Solve for \( x \)
1. **Subtract \( 5x \) from both sides:**
\[ 7x - 5x - 4 = 5x - 5x + 10 \]
\[ 2x - 4 = 10 \]
2. **Add 4 to both sides:**
\[ 2x - 4 + 4 = 10 + 4 \]
\[ 2x = 14 \]
3. **Divide both sides by 2:**
\[ \frac{2x}{2} = \frac{14}{2} \]
\[ x = 7 \]
### Conclusion
The value of \( x \) is \( 7 \).
**Answer**: \( x = 7 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb07f600e-c9a1-46d0-bace-e790106da902%2Fa6edd03b-b056-4952-b2fc-dbbd1f40cb22%2Fjc6fem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem Statement
**Given**: \( m \parallel n \), find the value of \( x \).
### Diagram Explanation
The diagram consists of two parallel lines labeled \( m \) and \( n \). A transversal line intersects these two parallel lines, creating several angles.
- On the upper parallel line \( m \), one of the angles formed by the transversal is labeled \( (7x - 4)^\circ \).
- On the lower parallel line \( n \), the corresponding angle formed by the transversal is labeled \( (5x + 10)^\circ \).
Since \( m \parallel n \) and the transversal intersects both lines, these corresponding angles are congruent, meaning they are equal to each other.
### Setup the Equation
Since corresponding angles are equal, we set the angles equal to each other:
\[ (7x - 4)^\circ = (5x + 10)^\circ \]
### Solve for \( x \)
1. **Subtract \( 5x \) from both sides:**
\[ 7x - 5x - 4 = 5x - 5x + 10 \]
\[ 2x - 4 = 10 \]
2. **Add 4 to both sides:**
\[ 2x - 4 + 4 = 10 + 4 \]
\[ 2x = 14 \]
3. **Divide both sides by 2:**
\[ \frac{2x}{2} = \frac{14}{2} \]
\[ x = 7 \]
### Conclusion
The value of \( x \) is \( 7 \).
**Answer**: \( x = 7 \)
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