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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Equations and Inequations
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Question
![### Problem: Finding the Value of \( x \)
Given \( m \parallel n \), find the value of \( x \).
#### Diagram Description
There is a diagram involving two parallel lines labeled \( m \) and \( n \) with a diagonal transversal line intersecting both of them. The intersection creates several angles. Among these, two corresponding angles are given:
- The angle on the left side of the transversal is labeled as \( (3x + 3)^\circ \).
- The angle on the right side of the transversal is labeled as \( 84^\circ \).
Since lines \( m \) and \( n \) are parallel, the corresponding angles must be congruent.
#### Instructions
To solve for \( x \):
1. Set up the equation based on the relationship of corresponding angles:
\[
(3x + 3)^\circ = 84^\circ
\]
2. Isolate \( x \) by solving the equation:
\[
3x + 3 = 84
\]
\[
3x = 81 \quad (\text{by subtracting 3 from both sides})
\]
\[
x = 27 \quad (\text{by dividing both sides by 3})
\]
### Answer Submission
You can input the value of \( x \) into the answer box provided:
\[ \text{Answer:} \quad x = \_\_\_\_ \]
[Submit Answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F771f2658-8605-469b-a68d-3599653f583c%2F0c17f16e-7874-46ca-b355-80d792e88b82%2F8t2m4_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem: Finding the Value of \( x \)
Given \( m \parallel n \), find the value of \( x \).
#### Diagram Description
There is a diagram involving two parallel lines labeled \( m \) and \( n \) with a diagonal transversal line intersecting both of them. The intersection creates several angles. Among these, two corresponding angles are given:
- The angle on the left side of the transversal is labeled as \( (3x + 3)^\circ \).
- The angle on the right side of the transversal is labeled as \( 84^\circ \).
Since lines \( m \) and \( n \) are parallel, the corresponding angles must be congruent.
#### Instructions
To solve for \( x \):
1. Set up the equation based on the relationship of corresponding angles:
\[
(3x + 3)^\circ = 84^\circ
\]
2. Isolate \( x \) by solving the equation:
\[
3x + 3 = 84
\]
\[
3x = 81 \quad (\text{by subtracting 3 from both sides})
\]
\[
x = 27 \quad (\text{by dividing both sides by 3})
\]
### Answer Submission
You can input the value of \( x \) into the answer box provided:
\[ \text{Answer:} \quad x = \_\_\_\_ \]
[Submit Answer]
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