Given \( m \parallel n \), find the value of \( x \) and \( y \). The provided diagram contains two parallel lines \( m \) and \( n \), intersected by a transversal line. The angles formed at the intersections are labeled with expressions involving variables \( x \) and \( y \). The angles are: 1. \( (2y + 19)^\circ \): This is the angle formed between the transversal and line \( m \). 2. \( (5x + 20)^\circ \): This is the angle formed between the transversal and line \( n \) near the bottom intersection. 3. \( (4x - 11)^\circ \): This is the angle adjacent to \( (2y + 19)^\circ \). Since \( m \parallel n \), the corresponding and alternate interior angles are equal. ### Steps to Find \( x \) and \( y \): 1. Identify the relationships between the angles: - \( (2y + 19)^\circ \) and \( (5x + 20)^\circ \) are corresponding angles. - \( (2y + 19)^\circ \) is supplementary to \( (4x - 11)^\circ \). 2. Set up equations based on these relationships: \[ 2y + 19 = 5x + 20 \] \[ 2y + 19 + 4x - 11 = 180^\circ \] 3. Simplify the equations: \[ 2y + 19 = 5x + 20 \] \[ 2y + 4x + 8 = 180 \] \[ 2y + 4x = 172 \] \[ y + 2x = 86 \] 4. Solve the system of equations to find \( x \) and \( y \): From \( 2y + 19 = 5x + 20 \): \[ 2y - 5x = 1 \] Combine the equations: \[ 2y - 5x = 1 \] \[ y + 2x = 86 \] By solving this system of linear equations, you can find the precise values of \( x \) and \( y \).
Given \( m \parallel n \), find the value of \( x \) and \( y \). The provided diagram contains two parallel lines \( m \) and \( n \), intersected by a transversal line. The angles formed at the intersections are labeled with expressions involving variables \( x \) and \( y \). The angles are: 1. \( (2y + 19)^\circ \): This is the angle formed between the transversal and line \( m \). 2. \( (5x + 20)^\circ \): This is the angle formed between the transversal and line \( n \) near the bottom intersection. 3. \( (4x - 11)^\circ \): This is the angle adjacent to \( (2y + 19)^\circ \). Since \( m \parallel n \), the corresponding and alternate interior angles are equal. ### Steps to Find \( x \) and \( y \): 1. Identify the relationships between the angles: - \( (2y + 19)^\circ \) and \( (5x + 20)^\circ \) are corresponding angles. - \( (2y + 19)^\circ \) is supplementary to \( (4x - 11)^\circ \). 2. Set up equations based on these relationships: \[ 2y + 19 = 5x + 20 \] \[ 2y + 19 + 4x - 11 = 180^\circ \] 3. Simplify the equations: \[ 2y + 19 = 5x + 20 \] \[ 2y + 4x + 8 = 180 \] \[ 2y + 4x = 172 \] \[ y + 2x = 86 \] 4. Solve the system of equations to find \( x \) and \( y \): From \( 2y + 19 = 5x + 20 \): \[ 2y - 5x = 1 \] Combine the equations: \[ 2y - 5x = 1 \] \[ y + 2x = 86 \] By solving this system of linear equations, you can find the precise values of \( x \) and \( y \).
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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![Given \( m \parallel n \), find the value of \( x \) and \( y \).
The provided diagram contains two parallel lines \( m \) and \( n \), intersected by a transversal line. The angles formed at the intersections are labeled with expressions involving variables \( x \) and \( y \).
The angles are:
1. \( (2y + 19)^\circ \): This is the angle formed between the transversal and line \( m \).
2. \( (5x + 20)^\circ \): This is the angle formed between the transversal and line \( n \) near the bottom intersection.
3. \( (4x - 11)^\circ \): This is the angle adjacent to \( (2y + 19)^\circ \).
Since \( m \parallel n \), the corresponding and alternate interior angles are equal.
### Steps to Find \( x \) and \( y \):
1. Identify the relationships between the angles:
- \( (2y + 19)^\circ \) and \( (5x + 20)^\circ \) are corresponding angles.
- \( (2y + 19)^\circ \) is supplementary to \( (4x - 11)^\circ \).
2. Set up equations based on these relationships:
\[ 2y + 19 = 5x + 20 \]
\[ 2y + 19 + 4x - 11 = 180^\circ \]
3. Simplify the equations:
\[ 2y + 19 = 5x + 20 \]
\[ 2y + 4x + 8 = 180 \]
\[ 2y + 4x = 172 \]
\[ y + 2x = 86 \]
4. Solve the system of equations to find \( x \) and \( y \):
From \( 2y + 19 = 5x + 20 \):
\[ 2y - 5x = 1 \]
Combine the equations:
\[ 2y - 5x = 1 \]
\[ y + 2x = 86 \]
By solving this system of linear equations, you can find the precise values of \( x \) and \( y \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb3dca1d-57a3-4839-be8e-2a543baf6bdb%2Fc553d75d-3cd1-4c60-8257-b3b3c3d40ae2%2F9iore9_processed.png&w=3840&q=75)
Transcribed Image Text:Given \( m \parallel n \), find the value of \( x \) and \( y \).
The provided diagram contains two parallel lines \( m \) and \( n \), intersected by a transversal line. The angles formed at the intersections are labeled with expressions involving variables \( x \) and \( y \).
The angles are:
1. \( (2y + 19)^\circ \): This is the angle formed between the transversal and line \( m \).
2. \( (5x + 20)^\circ \): This is the angle formed between the transversal and line \( n \) near the bottom intersection.
3. \( (4x - 11)^\circ \): This is the angle adjacent to \( (2y + 19)^\circ \).
Since \( m \parallel n \), the corresponding and alternate interior angles are equal.
### Steps to Find \( x \) and \( y \):
1. Identify the relationships between the angles:
- \( (2y + 19)^\circ \) and \( (5x + 20)^\circ \) are corresponding angles.
- \( (2y + 19)^\circ \) is supplementary to \( (4x - 11)^\circ \).
2. Set up equations based on these relationships:
\[ 2y + 19 = 5x + 20 \]
\[ 2y + 19 + 4x - 11 = 180^\circ \]
3. Simplify the equations:
\[ 2y + 19 = 5x + 20 \]
\[ 2y + 4x + 8 = 180 \]
\[ 2y + 4x = 172 \]
\[ y + 2x = 86 \]
4. Solve the system of equations to find \( x \) and \( y \):
From \( 2y + 19 = 5x + 20 \):
\[ 2y - 5x = 1 \]
Combine the equations:
\[ 2y - 5x = 1 \]
\[ y + 2x = 86 \]
By solving this system of linear equations, you can find the precise values of \( x \) and \( y \).
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