Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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ISBN: 9780547587776
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
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**Diagram Explanation:**
- The circle is divided into four sectors.
- The angles of each sector are given as follows:
- One sector has an angle of \( 48^\circ \).
- Another sector has an angle of \( 65^\circ \).
- The third sector is labeled \( 7x - 8 \) degrees.
- The fourth sector is labeled \( x \) degrees.
**Instructions:**
1. Recall that the sum of the central angles of a circle is \( 360^\circ \).
2. Set up the equation by adding all the angles and setting them equal to \( 360^\circ \).
\[
48^\circ + 65^\circ + (7x - 8)^\circ + x^\circ = 360^\circ
\]
3. Solve for \( x \):
Combine like terms:
\[
48 + 65 + 7x - 8 + x = 360
\]
This simplifies to:
\[
105 + 8x = 360
\]
Isolate \( 8x \):
\[
8x = 360 - 105
\]
\[
8x = 255
\]
Solve for \( x \):
\[
x = \frac{255}{8}
\]
\[
x = 31.875
\]
Therefore, the value of \( x \) is:
\[
x = 31.875
\]](https://content.bartleby.com/qna-images/question/34dbf93a-185c-4522-bbbf-f73f18b87311/8b0a585b-5255-4849-9c54-203718dcfdaa/4xnqnzo_processed.jpeg)
Transcribed Image Text:### 9.1 Mastery: Central Angles & Arcs
#### Objective: Find the value of \( x \).
The image below displays a circle divided into four sectors with central angles. The problem is to determine the value of \( x \).
**Diagram Explanation:**
- The circle is divided into four sectors.
- The angles of each sector are given as follows:
- One sector has an angle of \( 48^\circ \).
- Another sector has an angle of \( 65^\circ \).
- The third sector is labeled \( 7x - 8 \) degrees.
- The fourth sector is labeled \( x \) degrees.
**Instructions:**
1. Recall that the sum of the central angles of a circle is \( 360^\circ \).
2. Set up the equation by adding all the angles and setting them equal to \( 360^\circ \).
\[
48^\circ + 65^\circ + (7x - 8)^\circ + x^\circ = 360^\circ
\]
3. Solve for \( x \):
Combine like terms:
\[
48 + 65 + 7x - 8 + x = 360
\]
This simplifies to:
\[
105 + 8x = 360
\]
Isolate \( 8x \):
\[
8x = 360 - 105
\]
\[
8x = 255
\]
Solve for \( x \):
\[
x = \frac{255}{8}
\]
\[
x = 31.875
\]
Therefore, the value of \( x \) is:
\[
x = 31.875
\]
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