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### Problem Statement 2) Solve for \( m \overarc{FIG} \) ### Diagram Explanation The diagram provided is a circle with its center labeled as a point. The circle is divided into several sectors with the following labels and angle measures: - Sector \( \angle HIG \) is marked as \( 79^\circ \). - Sector \( \angle FIG \) is marked as \( 46^\circ \). - Other sectors are labeled as \( J \), \( F \), \( I \), and \( G \) but do not have angle measures provided. ### Solution Strategy To solve for \( m \overarc{FIG} \), which is the measure of the arc \( FIG \), follow these steps: 1. Identify the relevant sectors and their angle measures. 2. Recognize that the arc \( FIG \) is part of the circle which is divided into sectors that sum up to the total circle measure of \( 360^\circ \). 3. Use the angle measures provided within the circle to calculate the desired arc measure. ### Calculation From the given diagram: - The angle \( \angle FIG = 46^\circ \). The measure of the arc \( FIG \) is simply the angle measure at sector \( \angle FIG \). Thus, the measure of the arc \( FIG \) is \( 46^\circ \). ### Conclusion The measure of \( m \overarc{FIG} \) is \( 46^\circ \).

### Problem Statement 2) Solve for \( m \overarc{FIG} \) ### Diagram Explanation The diagram provided is a circle with its center labeled as a point. The circle is divided into several sectors with the following labels and angle measures: - Sector \( \angle HIG \) is marked as \( 79^\circ \). - Sector \( \angle FIG \) is marked as \( 46^\circ \). - Other sectors are labeled as \( J \), \( F \), \( I \), and \( G \) but do not have angle measures provided. ### Solution Strategy To solve for \( m \overarc{FIG} \), which is the measure of the arc \( FIG \), follow these steps: 1. Identify the relevant sectors and their angle measures. 2. Recognize that the arc \( FIG \) is part of the circle which is divided into sectors that sum up to the total circle measure of \( 360^\circ \). 3. Use the angle measures provided within the circle to calculate the desired arc measure. ### Calculation From the given diagram: - The angle \( \angle FIG = 46^\circ \). The measure of the arc \( FIG \) is simply the angle measure at sector \( \angle FIG \). Thus, the measure of the arc \( FIG \) is \( 46^\circ \). ### Conclusion The measure of \( m \overarc{FIG} \) is \( 46^\circ \).

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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### Problem Statement 2) Solve for \( m \overarc{FIG} \) ### Diagram Explanation The diagram provided is a circle with its center labeled as a point. The circle is divided into several sectors with the following labels and angle measures: - Sector \( \angle HIG \) is marked as \( 79^\circ \). - Sector \( \angle FIG \) is marked as \( 46^\circ \). - Other sectors are labeled as \( J \), \( F \), \( I \), and \( G \) but do not have angle measures provided. ### Solution Strategy To solve for \( m \overarc{FIG} \), which is the measure of the arc \( FIG \), follow these steps: 1. Identify the relevant sectors and their angle measures. 2. Recognize that the arc \( FIG \) is part of the circle which is divided into sectors that sum up to the total circle measure of \( 360^\circ \). 3. Use the angle measures provided within the circle to calculate the desired arc measure. ### Calculation From the given diagram: - The angle \( \angle FIG = 46^\circ \). The measure of the arc \( FIG \) is simply the angle measure at sector \( \angle FIG \). Thus, the measure of the arc \( FIG \) is \( 46^\circ \). ### Conclusion The measure of \( m \overarc{FIG} \) is \( 46^\circ \).
Transcribed Image Text:### Problem Statement 2) Solve for \( m \overarc{FIG} \) ### Diagram Explanation The diagram provided is a circle with its center labeled as a point. The circle is divided into several sectors with the following labels and angle measures: - Sector \( \angle HIG \) is marked as \( 79^\circ \). - Sector \( \angle FIG \) is marked as \( 46^\circ \). - Other sectors are labeled as \( J \), \( F \), \( I \), and \( G \) but do not have angle measures provided. ### Solution Strategy To solve for \( m \overarc{FIG} \), which is the measure of the arc \( FIG \), follow these steps: 1. Identify the relevant sectors and their angle measures. 2. Recognize that the arc \( FIG \) is part of the circle which is divided into sectors that sum up to the total circle measure of \( 360^\circ \). 3. Use the angle measures provided within the circle to calculate the desired arc measure. ### Calculation From the given diagram: - The angle \( \angle FIG = 46^\circ \). The measure of the arc \( FIG \) is simply the angle measure at sector \( \angle FIG \). Thus, the measure of the arc \( FIG \) is \( 46^\circ \). ### Conclusion The measure of \( m \overarc{FIG} \) is \( 46^\circ \).
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