### Problem Statement and Diagram - Transversal and Angles **8. Given:** - Parallel lines \( l \parallel m \) with a transversal \( t \) **Angles:** - \( m\angle1 = 5x + y \) - \( m\angle2 = 3x \) - \( m\angle3 = 3x + 5y \) **Objective:** Find the values of \( x \) and \( y \). **Diagram Explanation:** The diagram illustrates two parallel lines \( l \) and \( m \) which are intersected by a transversal \( t \). This creates several angles at the intersection points. The specific angles considered for the problem are labeled as \( \angle \)1, \( \angle \)2, and \( \angle \)3. 1. **Angle 1 (\( \angle1 \))**: This angle is where \( t \) intersects \( l \) on the left side of the transversal above line \( m \). 2. **Angle 2 (\( \angle2 \))**: This angle is directly below \( \angle1 \) at the intersection of \( t \) and \( m \) on the left side. 3. **Angle 3 (\( \angle3 \))**: This angle is directly opposite \( \angle1 \) where \( t \) intersects \( l \) on the right side of the transversal. The relationships given for these angles are: - \( \angle 1 \) has a measure of \( 5x + y \) - \( \angle 2 \) has a measure of \( 3x \) - \( \angle 3 \) has a measure of \( 3x + 5y \) **Task Explanation:** To find \( x \) and \( y \): 1. Utilize the angle relationships given by the transversal intersecting parallel lines. For example, corresponding angles, alternate interior angles, or alternate exterior angles are congruent. 2. Set up equations based on the relationships and solve the system of equations to find the values of \( x \) and \( y \).
### Problem Statement and Diagram - Transversal and Angles **8. Given:** - Parallel lines \( l \parallel m \) with a transversal \( t \) **Angles:** - \( m\angle1 = 5x + y \) - \( m\angle2 = 3x \) - \( m\angle3 = 3x + 5y \) **Objective:** Find the values of \( x \) and \( y \). **Diagram Explanation:** The diagram illustrates two parallel lines \( l \) and \( m \) which are intersected by a transversal \( t \). This creates several angles at the intersection points. The specific angles considered for the problem are labeled as \( \angle \)1, \( \angle \)2, and \( \angle \)3. 1. **Angle 1 (\( \angle1 \))**: This angle is where \( t \) intersects \( l \) on the left side of the transversal above line \( m \). 2. **Angle 2 (\( \angle2 \))**: This angle is directly below \( \angle1 \) at the intersection of \( t \) and \( m \) on the left side. 3. **Angle 3 (\( \angle3 \))**: This angle is directly opposite \( \angle1 \) where \( t \) intersects \( l \) on the right side of the transversal. The relationships given for these angles are: - \( \angle 1 \) has a measure of \( 5x + y \) - \( \angle 2 \) has a measure of \( 3x \) - \( \angle 3 \) has a measure of \( 3x + 5y \) **Task Explanation:** To find \( x \) and \( y \): 1. Utilize the angle relationships given by the transversal intersecting parallel lines. For example, corresponding angles, alternate interior angles, or alternate exterior angles are congruent. 2. Set up equations based on the relationships and solve the system of equations to find the 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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Transcribed Image Text:### Problem Statement and Diagram - Transversal and Angles
**8. Given:**
- Parallel lines \( l \parallel m \) with a transversal \( t \)
**Angles:**
- \( m\angle1 = 5x + y \)
- \( m\angle2 = 3x \)
- \( m\angle3 = 3x + 5y \)
**Objective:**
Find the values of \( x \) and \( y \).
**Diagram Explanation:**
The diagram illustrates two parallel lines \( l \) and \( m \) which are intersected by a transversal \( t \). This creates several angles at the intersection points. The specific angles considered for the problem are labeled as \( \angle \)1, \( \angle \)2, and \( \angle \)3.
1. **Angle 1 (\( \angle1 \))**: This angle is where \( t \) intersects \( l \) on the left side of the transversal above line \( m \).
2. **Angle 2 (\( \angle2 \))**: This angle is directly below \( \angle1 \) at the intersection of \( t \) and \( m \) on the left side.
3. **Angle 3 (\( \angle3 \))**: This angle is directly opposite \( \angle1 \) where \( t \) intersects \( l \) on the right side of the transversal.
The relationships given for these angles are:
- \( \angle 1 \) has a measure of \( 5x + y \)
- \( \angle 2 \) has a measure of \( 3x \)
- \( \angle 3 \) has a measure of \( 3x + 5y \)
**Task Explanation:**
To find \( x \) and \( y \):
1. Utilize the angle relationships given by the transversal intersecting parallel lines. For example, corresponding angles, alternate interior angles, or alternate exterior angles are congruent.
2. Set up equations based on the relationships and solve the system of equations to find the values of \( x \) and \( y \).
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