9. Find the arc length of the sector if the radius of the circle is 10 and the degree measure of the sectors central angle is 72°. Show work 10. Solve for x. show work. B. 106 (10x-23)
9. Find the arc length of the sector if the radius of the circle is 10 and the degree measure of the sectors central angle is 72°. Show work 10. Solve for x. show work. B. 106 (10x-23)
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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9 and 10 please
![### Math Problems on Circle Geometry
---
#### 9. Calculate the Arc Length of a Sector
**Problem Statement:**
Find the arc length of the sector if the radius of the circle is 10 and the degree measure of the sector's central angle is 72°. Show your work.
---
#### 10. Solve for \( x \)
**Problem Statement:**
Solve for \( x \). Show your work.
**Diagram Description:**
A circle is divided into two sectors by two radii \( \overline{AD} \) and \( \overline{DB} \). The sector \( \angle ABD = 10x - 23 \) degrees is adjacent to the other sector \( \angle BDC = 106 \) degrees. The point \( D \) is on the radius \( \overline{AC} \).
[Insert Image Here]
**Steps:**
1. Use the property that the sum of the angles in a circle is 360°.
Equation:
\( (10x - 23) + 106 + \angle ADC = 360° \)
2. Simplify and solve for \( \angle ADC \).
---
#### 11. Use the Diagram Below to Find the Measure of Each
**Diagram:**
This section includes various details to find the required measures based on a given diagram.
---
This educational exercise aims to build a solid understanding of basic geometry concepts related to circles, particularly focusing on arc lengths and angle measures within a circle. These steps will aid in comprehending and solving the involved geometry problems effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6756c5c2-608f-4015-b13f-deb910f8c3e1%2F33358c60-0c0c-447e-b78a-3433c0a38c56%2F39pva9r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Math Problems on Circle Geometry
---
#### 9. Calculate the Arc Length of a Sector
**Problem Statement:**
Find the arc length of the sector if the radius of the circle is 10 and the degree measure of the sector's central angle is 72°. Show your work.
---
#### 10. Solve for \( x \)
**Problem Statement:**
Solve for \( x \). Show your work.
**Diagram Description:**
A circle is divided into two sectors by two radii \( \overline{AD} \) and \( \overline{DB} \). The sector \( \angle ABD = 10x - 23 \) degrees is adjacent to the other sector \( \angle BDC = 106 \) degrees. The point \( D \) is on the radius \( \overline{AC} \).
[Insert Image Here]
**Steps:**
1. Use the property that the sum of the angles in a circle is 360°.
Equation:
\( (10x - 23) + 106 + \angle ADC = 360° \)
2. Simplify and solve for \( \angle ADC \).
---
#### 11. Use the Diagram Below to Find the Measure of Each
**Diagram:**
This section includes various details to find the required measures based on a given diagram.
---
This educational exercise aims to build a solid understanding of basic geometry concepts related to circles, particularly focusing on arc lengths and angle measures within a circle. These steps will aid in comprehending and solving the involved geometry problems effectively.
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