O 50 5x+5 к Findx Т S 2x+10

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:
     \[
     7x + 15 = 50
     \]
     \[
     7x = 35
     \]
     \[
     x = 5
     \]

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### 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:
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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