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1. In circle with MNP = 12 a, find the %3D

1. In circle with MNP = 12 a, find the %3D

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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### Geometry Problem **Problem Statement:** In circle \( N \) with \(\angle MNP = 120^\circ\), find the measure of arc \( MQP \). **Diagram Explanation:** The diagram shows a circle labeled \( N \). Inside the circle, three points \( M, N, \) and \( P \) are marked on the circumference. There is an arc from \( M \) to \( P \) passing through \( Q \). The angle \( MNP \) is given as \( 120^\circ \). - \(M\) and \(P\) are points where the chord intersects the circumference at two places. - \(N\) is the center of the circle. - The angle \(\angle MNP\) formed at the center by points \( M \) and \( P \) is \( 120^\circ \). ### Steps to Solve: 1. **Identify the Given Angle:** - The central angle \(\angle MNP\) is \(120^\circ\). 2. **Understanding Arc Measure:** - The measure of the arc is directly related to its corresponding central angle. In a circle, the measure of the arc is equal to the central angle that subtends it. 3. **Calculate Arc \( MQP \):** - Since \(\angle MNP\) is \(120^\circ\), the measure of arc \( MQP \) is also \(120^\circ\). **Answer:** The measure of arc \( MQP \) is \( 120^\circ \).
Transcribed Image Text:### Geometry Problem **Problem Statement:** In circle \( N \) with \(\angle MNP = 120^\circ\), find the measure of arc \( MQP \). **Diagram Explanation:** The diagram shows a circle labeled \( N \). Inside the circle, three points \( M, N, \) and \( P \) are marked on the circumference. There is an arc from \( M \) to \( P \) passing through \( Q \). The angle \( MNP \) is given as \( 120^\circ \). - \(M\) and \(P\) are points where the chord intersects the circumference at two places. - \(N\) is the center of the circle. - The angle \(\angle MNP\) formed at the center by points \( M \) and \( P \) is \( 120^\circ \). ### Steps to Solve: 1. **Identify the Given Angle:** - The central angle \(\angle MNP\) is \(120^\circ\). 2. **Understanding Arc Measure:** - The measure of the arc is directly related to its corresponding central angle. In a circle, the measure of the arc is equal to the central angle that subtends it. 3. **Calculate Arc \( MQP \):** - Since \(\angle MNP\) is \(120^\circ\), the measure of arc \( MQP \) is also \(120^\circ\). **Answer:** The measure of arc \( MQP \) is \( 120^\circ \).
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