In circle P with the measure of minor arc NQ= 120°, find mZNRQ. N R

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
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### Arc Measure

**Date:** Jun 18, 2:38:24 AM

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#### Problem Statement:
In circle \( P \) with the measure of minor arc \( \overset{\frown}{NQ} = 120^{\circ} \), find \( m \angle NRQ \).

#### Diagram Explanation:
- The given diagram represents a circle with center \( P \).
- Points \( N \), \( Q \), and \( R \) are on the circumference of the circle.
- The minor arc \( \overset{\frown}{NQ} \) is marked, and its measure is given as \( 120^{\circ} \).
- Line segments \( NP \) and \( NR \) are radii of the circle, where segment \( NR \) is not perpendicular to the arc’s chord. 
- The angle \( \angle NRQ \) is formed by the intersection of line segments \( NR \) and \( RQ \).

Using this information and applying the properties of circles, specifically the relationship between central angles and inscribed angles, can help find the measure of the desired angle \( \angle NRQ \).
Transcribed Image Text:### Arc Measure **Date:** Jun 18, 2:38:24 AM --- ### Watch Help Video --- #### Problem Statement: In circle \( P \) with the measure of minor arc \( \overset{\frown}{NQ} = 120^{\circ} \), find \( m \angle NRQ \). #### Diagram Explanation: - The given diagram represents a circle with center \( P \). - Points \( N \), \( Q \), and \( R \) are on the circumference of the circle. - The minor arc \( \overset{\frown}{NQ} \) is marked, and its measure is given as \( 120^{\circ} \). - Line segments \( NP \) and \( NR \) are radii of the circle, where segment \( NR \) is not perpendicular to the arc’s chord. - The angle \( \angle NRQ \) is formed by the intersection of line segments \( NR \) and \( RQ \). Using this information and applying the properties of circles, specifically the relationship between central angles and inscribed angles, can help find the measure of the desired angle \( \angle NRQ \).
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