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M 82/63 P. Q MQ and NR are diameters. Find the indicated measure. arc NQ

M 82/63 P. Q MQ and NR are diameters. Find the indicated measure. arc NQ

Elementary Geometry For College Students, 7e
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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### 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°]
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°]
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