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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![**Educational Website Transcription**
Welcome to the Geometry Practice Section!
In this section, we will focus on solving for unknown variables in geometric diagrams. Here are a few examples for you to work through.
-------------------------------------------------------------
### Example 1: Solving for x
1. **Problem:**
- Given a geometric figure with three line segments and variables, find the value of x.
- Diagram details:
- Three points, labeled K, S, and T, form parts of the figure.
- KS segment is labeled as \( 5x + 5 \).
- ST segment is labeled as \( 2x + 10 \).
- The total length of KT is given as 50.
- To solve for x, set up the equation based on the given information:
\[
5x + 5 + 2x + 10 = 50
\]
Simplify and solve for x:
\[
7x + 15 = 50
\]
\[
7x = 35
\]
\[
x = 5
\]
-------------------------------------------------------------
### Example 2: Solving for an angle
2. **Problem:**
- Given a geometric figure with an angle, calculate the value of the angle.
- Diagram details:
- Angle at point O, labeled as \( \angle AOC \), is divided into two parts.
- One part of the angle is labeled \( (45 - x)^\circ \), and the other part is labeled simply.
- To solve for the angle, you may need to know additional details not provided in the image. Generally, these solutions would involve usage of angle relationships and algebra to find x.
-------------------------------------------------------------
### Example 3: Bisected angle
3. **Problem:**
- Given that line segment OB bisects \( \angle AOC \).
- Diagram details:
- Points A, B, and C form vectors starting from point O.
- The angles created are labeled:
- \( m \angle AOB = 11x - 3 \)
- \( m \angle BOC = 7x + 9 \)
- Since OB is the bisector, the sum of these two angles equal \( \angle AOC \).
- Set up the equation based on sum of angles:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00c239b2-49f2-4118-83c1-4fc31b3c935a%2Fded520b8-f201-4128-8005-5af77f6e293b%2Fpzgnv7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Transcription**
Welcome to the Geometry Practice Section!
In this section, we will focus on solving for unknown variables in geometric diagrams. Here are a few examples for you to work through.
-------------------------------------------------------------
### Example 1: Solving for x
1. **Problem:**
- Given a geometric figure with three line segments and variables, find the value of x.
- Diagram details:
- Three points, labeled K, S, and T, form parts of the figure.
- KS segment is labeled as \( 5x + 5 \).
- ST segment is labeled as \( 2x + 10 \).
- The total length of KT is given as 50.
- To solve for x, set up the equation based on the given information:
\[
5x + 5 + 2x + 10 = 50
\]
Simplify and solve for x:
\[
7x + 15 = 50
\]
\[
7x = 35
\]
\[
x = 5
\]
-------------------------------------------------------------
### Example 2: Solving for an angle
2. **Problem:**
- Given a geometric figure with an angle, calculate the value of the angle.
- Diagram details:
- Angle at point O, labeled as \( \angle AOC \), is divided into two parts.
- One part of the angle is labeled \( (45 - x)^\circ \), and the other part is labeled simply.
- To solve for the angle, you may need to know additional details not provided in the image. Generally, these solutions would involve usage of angle relationships and algebra to find x.
-------------------------------------------------------------
### Example 3: Bisected angle
3. **Problem:**
- Given that line segment OB bisects \( \angle AOC \).
- Diagram details:
- Points A, B, and C form vectors starting from point O.
- The angles created are labeled:
- \( m \angle AOB = 11x - 3 \)
- \( m \angle BOC = 7x + 9 \)
- Since OB is the bisector, the sum of these two angles equal \( \angle AOC \).
- Set up the equation based on sum of angles:
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