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
Related questions
Question
![### Understanding Circle Properties and Diameters
In this exercise, we have a circle centered at point O with two diameters, MQ and NR. The goal is to find the measure of the arc NQ.
#### Diagram Explanation:
1. **Circle Anatomy**:
- Point O is the center of the circle.
- MQ and NR are diameters of the circle, meaning they each span from one side of the circle to the other, passing through the center.
- The circle includes arc segments labeled with angle measures.
2. **Angle Information**:
- The angle ∠NOQ is marked as 82°.
- The angle ∠QOP is marked as 63°.
### Problem Statement:
"**MQ and NR are diameters. Find the indicated measure.**
**arc NQ:**
[Blank Space for Answer]"
#### Steps to Solve:
1. **Understanding Arcs and Angles**:
- In a circle, the sum of angles around a point (the center in this case) is 360°.
- The measure of arc NQ can be found by summing up the central angles ∠NOQ and ∠QOP that are subtended by arc NQ.
2. **Calculating the Arc Measure**:
- The measure of arc NQ is simply the sum of the central angles ∠NOQ (82°) and ∠QOP (63°).
Therefore,
\[
\text{arc NQ} = ∠NOQ + ∠QOP = 82° + 63° = 145°
\]
### Conclusion:
The measure of the arc NQ is 145°. This is because it is the sum of the given central angles that form the arc NQ in the circle.
[Blank Space for Answer: 145°]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff88ee4da-cab0-444b-92d4-30b9e0152253%2F15f439fe-f90f-462f-af50-7d9844e59ba3%2Fx85ox5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Circle Properties and Diameters
In this exercise, we have a circle centered at point O with two diameters, MQ and NR. The goal is to find the measure of the arc NQ.
#### Diagram Explanation:
1. **Circle Anatomy**:
- Point O is the center of the circle.
- MQ and NR are diameters of the circle, meaning they each span from one side of the circle to the other, passing through the center.
- The circle includes arc segments labeled with angle measures.
2. **Angle Information**:
- The angle ∠NOQ is marked as 82°.
- The angle ∠QOP is marked as 63°.
### Problem Statement:
"**MQ and NR are diameters. Find the indicated measure.**
**arc NQ:**
[Blank Space for Answer]"
#### Steps to Solve:
1. **Understanding Arcs and Angles**:
- In a circle, the sum of angles around a point (the center in this case) is 360°.
- The measure of arc NQ can be found by summing up the central angles ∠NOQ and ∠QOP that are subtended by arc NQ.
2. **Calculating the Arc Measure**:
- The measure of arc NQ is simply the sum of the central angles ∠NOQ (82°) and ∠QOP (63°).
Therefore,
\[
\text{arc NQ} = ∠NOQ + ∠QOP = 82° + 63° = 145°
\]
### Conclusion:
The measure of the arc NQ is 145°. This is because it is the sum of the given central angles that form the arc NQ in the circle.
[Blank Space for Answer: 145°]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 5 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning