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
Related questions
Question
![**Problem Statement:**
Find the values of \( x \) and \( y \).
**Diagram Explanation:**
The diagram presents two intersecting lines, creating four angles. The angles are expressed in terms of \( x \) and \( y \):
- The top left angle is labeled \( 4x^\circ \).
- The top right angle is labeled \( (7y - 12)^\circ \).
- The bottom left angle is labeled \( (6y + 8)^\circ \).
- The bottom right angle is labeled \( (6x - 26)^\circ \).
**Solution Approach:**
1. **Identify Vertical Angles:**
- Vertical angles are equal. Thus, the angles \( 4x^\circ \) and \( (6x - 26)^\circ \) are vertical and equal.
- Set the equation:
\[
4x = 6x - 26
\]
2. **Solve for \( x \):**
- Rearrange and solve:
\[
4x = 6x - 26
\]
\[
26 = 6x - 4x
\]
\[
26 = 2x
\]
\[
x = 13
\]
3. **Identify Additional Vertical Angles:**
- Similarly, angles \( (7y - 12)^\circ \) and \( (6y + 8)^\circ \) are vertical and therefore equal.
- Set the equation:
\[
7y - 12 = 6y + 8
\]
4. **Solve for \( y \):**
- Rearrange and solve:
\[
7y - 12 = 6y + 8
\]
\[
7y - 6y = 8 + 12
\]
\[
y = 20
\]
**Conclusion:**
The values of \( x \) and \( y \) are \( x = 13 \) and \( y = 20 \) respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F797dc8e7-34bf-4ddf-be4a-57a16dba5411%2Ff30cca1c-bcfc-4280-924f-be97347343a2%2F52yxr4_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the values of \( x \) and \( y \).
**Diagram Explanation:**
The diagram presents two intersecting lines, creating four angles. The angles are expressed in terms of \( x \) and \( y \):
- The top left angle is labeled \( 4x^\circ \).
- The top right angle is labeled \( (7y - 12)^\circ \).
- The bottom left angle is labeled \( (6y + 8)^\circ \).
- The bottom right angle is labeled \( (6x - 26)^\circ \).
**Solution Approach:**
1. **Identify Vertical Angles:**
- Vertical angles are equal. Thus, the angles \( 4x^\circ \) and \( (6x - 26)^\circ \) are vertical and equal.
- Set the equation:
\[
4x = 6x - 26
\]
2. **Solve for \( x \):**
- Rearrange and solve:
\[
4x = 6x - 26
\]
\[
26 = 6x - 4x
\]
\[
26 = 2x
\]
\[
x = 13
\]
3. **Identify Additional Vertical Angles:**
- Similarly, angles \( (7y - 12)^\circ \) and \( (6y + 8)^\circ \) are vertical and therefore equal.
- Set the equation:
\[
7y - 12 = 6y + 8
\]
4. **Solve for \( y \):**
- Rearrange and solve:
\[
7y - 12 = 6y + 8
\]
\[
7y - 6y = 8 + 12
\]
\[
y = 20
\]
**Conclusion:**
The values of \( x \) and \( y \) are \( x = 13 \) and \( y = 20 \) respectively.
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