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
![### Finding the Measure of Arc NQ
**Problem Statement:**
Given the circle diagram with points M, N, R, P, Q, and the center O, where MQ and NR are diameters, find the measure of arc NQ.
**Diagram Explanation:**
In the circle:
- Points M, N, R, P, and Q are on the circumference.
- MQ and NR are diameters, meaning they pass through the center O and divide the circle into two equal halves.
- Angle MON is given as 82 degrees.
- Angle NOR is given as 63 degrees.
### Calculation:
To find the measure of arc NQ, follow these steps:
1. **Calculate Central Angle of Remaining Arc:**
Since MQ and NR are diameters, the sum of all angles around O is 360 degrees.
Given:
- Angle MON = 82 degrees
- Angle NOR = 63 degrees
The remaining central angle PRO:
\[
\text{Angle PRO} = 360^\circ - 82^\circ - 63^\circ = 215^\circ
\]
2. **Determine the Measure of Arc NQ:**
The arc NQ corresponds to the central angle NOR which is across points N and Q.
So, the measure of arc NQ is equal to the measure of central angle NOR, which is:
\[
\text{Arc NQ} = 63^\circ
\]
**Answer:**
The measure of arc NQ is \( 63^\circ \).
**Interactive Question:**
You may fill in the measure of arc NQ below for verification.
**Input Box:**
```plaintext
arc NQ: 63°
```
Once the value is entered, you may click "OK" to check your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff88ee4da-cab0-444b-92d4-30b9e0152253%2F7d3a5552-b75f-40fb-9ee8-fef65a93444f%2Fz25t9lh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Measure of Arc NQ
**Problem Statement:**
Given the circle diagram with points M, N, R, P, Q, and the center O, where MQ and NR are diameters, find the measure of arc NQ.
**Diagram Explanation:**
In the circle:
- Points M, N, R, P, and Q are on the circumference.
- MQ and NR are diameters, meaning they pass through the center O and divide the circle into two equal halves.
- Angle MON is given as 82 degrees.
- Angle NOR is given as 63 degrees.
### Calculation:
To find the measure of arc NQ, follow these steps:
1. **Calculate Central Angle of Remaining Arc:**
Since MQ and NR are diameters, the sum of all angles around O is 360 degrees.
Given:
- Angle MON = 82 degrees
- Angle NOR = 63 degrees
The remaining central angle PRO:
\[
\text{Angle PRO} = 360^\circ - 82^\circ - 63^\circ = 215^\circ
\]
2. **Determine the Measure of Arc NQ:**
The arc NQ corresponds to the central angle NOR which is across points N and Q.
So, the measure of arc NQ is equal to the measure of central angle NOR, which is:
\[
\text{Arc NQ} = 63^\circ
\]
**Answer:**
The measure of arc NQ is \( 63^\circ \).
**Interactive Question:**
You may fill in the measure of arc NQ below for verification.
**Input Box:**
```plaintext
arc NQ: 63°
```
Once the value is entered, you may click "OK" to check your answer.
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