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
Related questions
Question
In the given diagram, there are two parallel lines labeled \( m \) and \( n \), intersected by a transversal line \( t \).
### Angles Details:
- On the upper side of the transversal \( t \):
- The angle between line \( t \) and line \( m \) is labeled as \( (4x - 13)^\circ \).
- On the lower side of the transversal \( t \):
- The angle between line \( t \) and line \( n \) is labeled as \( (x + 8)^\circ \).
### Explanation:
Since lines \( m \) and \( n \) are parallel and intersected by transversal \( t \), the angles \( (4x - 13)^\circ \) and \( (x + 8)^\circ \) form corresponding angles. Corresponding angles are equal when the lines are parallel.
Thus, we can set up the following equation:
\[ (4x - 13) = (x + 8) \]
### Solving for \( x \):
1. Subtract \( x \) from both sides:
\[ 4x - x - 13 = 8 \]
\[ 3x - 13 = 8 \]
2. Add 13 to both sides:
\[ 3x = 21 \]
3. Divide by 3:
\[ x = 7 \]
Therefore, the value of \( x \) is \( 7 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb3dca1d-57a3-4839-be8e-2a543baf6bdb%2Fc0ba03a4-cab1-4845-bbdc-6f531ac8a60c%2Fwp6f6o9_processed.png&w=3840&q=75)
Transcribed Image Text:**Given \( m \parallel n \), find the value of \( x \).**
In the given diagram, there are two parallel lines labeled \( m \) and \( n \), intersected by a transversal line \( t \).
### Angles Details:
- On the upper side of the transversal \( t \):
- The angle between line \( t \) and line \( m \) is labeled as \( (4x - 13)^\circ \).
- On the lower side of the transversal \( t \):
- The angle between line \( t \) and line \( n \) is labeled as \( (x + 8)^\circ \).
### Explanation:
Since lines \( m \) and \( n \) are parallel and intersected by transversal \( t \), the angles \( (4x - 13)^\circ \) and \( (x + 8)^\circ \) form corresponding angles. Corresponding angles are equal when the lines are parallel.
Thus, we can set up the following equation:
\[ (4x - 13) = (x + 8) \]
### Solving for \( x \):
1. Subtract \( x \) from both sides:
\[ 4x - x - 13 = 8 \]
\[ 3x - 13 = 8 \]
2. Add 13 to both sides:
\[ 3x = 21 \]
3. Divide by 3:
\[ x = 7 \]
Therefore, the value of \( x \) is \( 7 \).
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