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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Help on #6
![### Solving for the Missing Value in a Circle Diagram
#### Problem Statement:
Use the figure below to find the missing value.
#### Figure Explanation:
The provided figure is a circle with four segments labeled with the following expressions and values:
- One segment is labeled \( 12 \).
- One segment is labeled \( 2x - 10 \).
- One segment is labeled \( 16 \).
- One segment is labeled \( x + 10 \).
#### Diagram:
(The user should imagine a circle divided into four sections. The values and expressions are placed inside each section.)
#### Solution Choices:
A. \( x = 14 \)
B. \( x = 6.36 \)
C. \( x = 35 \)
D. \( x = 16 \) *(this choice is marked as the selected one)*
#### Solving the Equation:
1. To find the missing value \( x \), we need to use the fact that the sum of all four segments in a circle must be equal to the total angle around a point, which is 360 degrees.
2. Therefore, we set up the equation with the given segments:
\[
12 + (2x - 10) + 16 + (x + 10) = 360
\]
3. Simplify the equation:
\[
12 + 2x - 10 + 16 + x + 10 = 360
\]
\[
2x + x + 12 - 10 + 16 + 10 = 360
\]
\[
3x + 28 = 360
\]
4. Solve for \( x \):
\[
3x + 28 - 28 = 360 - 28
\]
\[
3x = 332
\]
\[
x = \frac{332}{3}
\]
\[
x = 110.\overline{6}
\]
Upon reflecting on the calculation, it seems there may have been an error or misunderstanding in the setup of the problem, as the solution provided (D. \( x = 16 \)) is not aligning with the arithmetic solution found above. Thus, a re-evaluation is necessary to ensure continuity with the figure's properties and alignment with the given choices.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4904ad93-6dcc-43fa-9122-8f69394907f2%2F5984affc-059a-40dd-bf16-9a9aac9b9c3d%2Fsyyc2zs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving for the Missing Value in a Circle Diagram
#### Problem Statement:
Use the figure below to find the missing value.
#### Figure Explanation:
The provided figure is a circle with four segments labeled with the following expressions and values:
- One segment is labeled \( 12 \).
- One segment is labeled \( 2x - 10 \).
- One segment is labeled \( 16 \).
- One segment is labeled \( x + 10 \).
#### Diagram:
(The user should imagine a circle divided into four sections. The values and expressions are placed inside each section.)
#### Solution Choices:
A. \( x = 14 \)
B. \( x = 6.36 \)
C. \( x = 35 \)
D. \( x = 16 \) *(this choice is marked as the selected one)*
#### Solving the Equation:
1. To find the missing value \( x \), we need to use the fact that the sum of all four segments in a circle must be equal to the total angle around a point, which is 360 degrees.
2. Therefore, we set up the equation with the given segments:
\[
12 + (2x - 10) + 16 + (x + 10) = 360
\]
3. Simplify the equation:
\[
12 + 2x - 10 + 16 + x + 10 = 360
\]
\[
2x + x + 12 - 10 + 16 + 10 = 360
\]
\[
3x + 28 = 360
\]
4. Solve for \( x \):
\[
3x + 28 - 28 = 360 - 28
\]
\[
3x = 332
\]
\[
x = \frac{332}{3}
\]
\[
x = 110.\overline{6}
\]
Upon reflecting on the calculation, it seems there may have been an error or misunderstanding in the setup of the problem, as the solution provided (D. \( x = 16 \)) is not aligning with the arithmetic solution found above. Thus, a re-evaluation is necessary to ensure continuity with the figure's properties and alignment with the given choices.
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