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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Question
![**Problem Statement:**
Given \( m \parallel n \), find the value of \( x \) and \( y \).
**Diagram Explanation:**
The image shows two parallel lines, \( m \) and \( n \), with a transversal line intersecting them. There are three angle expressions marked:
1. The angle between the transversal and line \( m \) is labeled as \( (5x + 9)^\circ \).
2. The angle between the transversal and line \( n \) is labeled as \( (4x + 17)^\circ \).
3. There is another angle on line \( n \) labeled as \( (y + 20)^\circ \).
**Calculations:**
To find the values of \( x \) and \( y \), use the properties of parallel lines and corresponding angles:
- Since \( m \parallel n \), the corresponding angles are equal. Therefore, set the expressions for corresponding angles equal to each other:
\[
5x + 9 = 4x + 17
\]
Solving this equation will give you the value of \( x \).
- To find \( y \), use the fact that the angle \( (y + 20)^\circ \) is supplementary to the angle \( (4x + 17)^\circ \) because they are on a straight line intersected by the transversal.
\[
(4x + 17) + (y + 20) = 180
\]
Plug the value of \( x \) from the first equation into this equation to solve for \( y \).
**Input Fields:**
- \( x = \) [Input box for \( x \)]
- \( y = \) [Input box for \( y \)]
**Submit Button:**
- [Submit Answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbae10b4-4609-4da0-ac46-fd2b6e5095b5%2Fd112dbc3-b53f-469c-9a80-e974da83c610%2Flhmr3pl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given \( m \parallel n \), find the value of \( x \) and \( y \).
**Diagram Explanation:**
The image shows two parallel lines, \( m \) and \( n \), with a transversal line intersecting them. There are three angle expressions marked:
1. The angle between the transversal and line \( m \) is labeled as \( (5x + 9)^\circ \).
2. The angle between the transversal and line \( n \) is labeled as \( (4x + 17)^\circ \).
3. There is another angle on line \( n \) labeled as \( (y + 20)^\circ \).
**Calculations:**
To find the values of \( x \) and \( y \), use the properties of parallel lines and corresponding angles:
- Since \( m \parallel n \), the corresponding angles are equal. Therefore, set the expressions for corresponding angles equal to each other:
\[
5x + 9 = 4x + 17
\]
Solving this equation will give you the value of \( x \).
- To find \( y \), use the fact that the angle \( (y + 20)^\circ \) is supplementary to the angle \( (4x + 17)^\circ \) because they are on a straight line intersected by the transversal.
\[
(4x + 17) + (y + 20) = 180
\]
Plug the value of \( x \) from the first equation into this equation to solve for \( y \).
**Input Fields:**
- \( x = \) [Input box for \( x \)]
- \( y = \) [Input box for \( y \)]
**Submit Button:**
- [Submit Answer]
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