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
![**Exercise: Solve for x**
**Diagram Explanation:**
The diagram represents an angle bisector. The line segment \(\overline{AB}\) acts as an angle bisector, meaning it divides the angle into two equal parts.
- The angle ∠A on the left is split into two parts:
- The top part of the angle is labeled \((5x + 9)^\circ\).
- The bottom part of the angle is labeled \((7x - 5)^\circ\).
Given information:
- \(\overline{AB}\) is an angle bisector.
Since \(\overline{AB}\) is an angle bisector, the two angles are equal. Therefore, we can set up the following equation to solve for \(x\):
\[5x + 9 = 7x - 5\]
To solve this equation:
1. Subtract \(5x\) from both sides:
\[9 = 2x - 5\]
2. Add 5 to both sides:
\[14 = 2x\]
3. Divide by 2:
\[x = 7\]
So, the value of \( x \) is \( 7 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20047395-754f-4b4f-b55f-051358973abe%2Fd15cfa81-4531-4754-91c4-fe693c8f3c98%2Fvlidyo3.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise: Solve for x**
**Diagram Explanation:**
The diagram represents an angle bisector. The line segment \(\overline{AB}\) acts as an angle bisector, meaning it divides the angle into two equal parts.
- The angle ∠A on the left is split into two parts:
- The top part of the angle is labeled \((5x + 9)^\circ\).
- The bottom part of the angle is labeled \((7x - 5)^\circ\).
Given information:
- \(\overline{AB}\) is an angle bisector.
Since \(\overline{AB}\) is an angle bisector, the two angles are equal. Therefore, we can set up the following equation to solve for \(x\):
\[5x + 9 = 7x - 5\]
To solve this equation:
1. Subtract \(5x\) from both sides:
\[9 = 2x - 5\]
2. Add 5 to both sides:
\[14 = 2x\]
3. Divide by 2:
\[x = 7\]
So, the value of \( x \) is \( 7 \).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning