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
![**Geometry Problem: Solving for x**
**Problem Statement:**
The two lines below intersect as shown. What is the value of x?
**Diagram Explanation:**
The diagram shows two intersecting lines forming an X shape. At the top left of the intersection, the angle is labeled \((2x + 29)^\circ\). At the top right of the intersection, the angle is labeled \((9x - 13)^\circ\).
\[(2x + 29)^\circ \quad (9x - 13)^\circ\]
The possible answer choices are:
- 6
- 9
- 12
- 4
**Details for Calculation:**
Given that the angles opposite each other are congruent, the equation to solve for \(x\) is:
\[2x + 29 = 9x - 13\]
Solving for \(x\):
1. Subtract \(2x\) from both sides:
\[29 = 7x - 13\]
2. Add 13 to both sides:
\[42 = 7x\]
3. Divide both sides by 7:
\[x = 6\]
Therefore, the correct value of \(x\) is 6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7245aef9-c798-4f68-8116-7b90c3c18a0a%2Fd448751f-ccbc-4d31-a0c9-dd50a9efedf1%2F3asoiba_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Geometry Problem: Solving for x**
**Problem Statement:**
The two lines below intersect as shown. What is the value of x?
**Diagram Explanation:**
The diagram shows two intersecting lines forming an X shape. At the top left of the intersection, the angle is labeled \((2x + 29)^\circ\). At the top right of the intersection, the angle is labeled \((9x - 13)^\circ\).
\[(2x + 29)^\circ \quad (9x - 13)^\circ\]
The possible answer choices are:
- 6
- 9
- 12
- 4
**Details for Calculation:**
Given that the angles opposite each other are congruent, the equation to solve for \(x\) is:
\[2x + 29 = 9x - 13\]
Solving for \(x\):
1. Subtract \(2x\) from both sides:
\[29 = 7x - 13\]
2. Add 13 to both sides:
\[42 = 7x\]
3. Divide both sides by 7:
\[x = 6\]
Therefore, the correct value of \(x\) is 6.
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