EasyBib: Fre 9.1 Mastery: Central Angles & Arcs Find x. 48 7x-S 6S
ChapterP: Prerequisites
SectionP.6: The Rectangular Coordinate System And Graphs
Problem 37E: An airplane flies from Naples, Italy, in a straight line to Rome, Italy, which is 120 kilometers...
Related questions
Question
**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:
\[
x = 31.875
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34dbf93a-185c-4522-bbbf-f73f18b87311%2F8b0a585b-5255-4849-9c54-203718dcfdaa%2F4xnqnzo_processed.jpeg&w=3840&q=75)
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:
\[
x = 31.875
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
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, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University