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Find the measure of arc PJ. L 82 ° 78 ° K

Find the measure of arc PJ. L 82 ° 78 ° K

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: Finding the Measure of an Arc** **Problem Statement:** Find the measure of arc \( PJ \). **Graph Description:** A circle is presented with four points on its circumference labeled as \( P \), \( L \), \( K \), and \( J \). A central point, marked as \( M \), is connected to the points on the circumference with lines forming angles at \( M \). **Detailed Angles Provided:** - Intersection at point \( M \) right between \( L \) and \( M \) is an angle of \( 78^\circ \). - Intersection at point \( M \) right between \( K \) and \( M \) is an angle of \( 82^\circ \). The task is to find the measure of the arc \( PJ \), which is drawn connecting points \( P \) and \( J \) along the circle's circumference. **How to Solve:** 1. Determine the total measure of the circle which is \( 360^\circ \). 2. Subtract the sum of the given angles from \( 360^\circ \): - The sum of the given angles: \( 78^\circ + 82^\circ = 160^\circ \). - Total remaining degrees: \( 360^\circ - 160^\circ = 200^\circ \). Therefore, the measure of arc \( PJ \) is \( 200^\circ \). **Conclusion:** The measure of arc \( PJ \) is \( 200^\circ \). **Navigation Options:** Use the 'Previous' button to revisit prior problems, or select any of the numbers from 1 to 12 to navigate to specific questions within the series. This will help in reviewing or skipping to different parts of the problem set according to necessity.
Transcribed Image Text:**Geometry Problem: Finding the Measure of an Arc** **Problem Statement:** Find the measure of arc \( PJ \). **Graph Description:** A circle is presented with four points on its circumference labeled as \( P \), \( L \), \( K \), and \( J \). A central point, marked as \( M \), is connected to the points on the circumference with lines forming angles at \( M \). **Detailed Angles Provided:** - Intersection at point \( M \) right between \( L \) and \( M \) is an angle of \( 78^\circ \). - Intersection at point \( M \) right between \( K \) and \( M \) is an angle of \( 82^\circ \). The task is to find the measure of the arc \( PJ \), which is drawn connecting points \( P \) and \( J \) along the circle's circumference. **How to Solve:** 1. Determine the total measure of the circle which is \( 360^\circ \). 2. Subtract the sum of the given angles from \( 360^\circ \): - The sum of the given angles: \( 78^\circ + 82^\circ = 160^\circ \). - Total remaining degrees: \( 360^\circ - 160^\circ = 200^\circ \). Therefore, the measure of arc \( PJ \) is \( 200^\circ \). **Conclusion:** The measure of arc \( PJ \) is \( 200^\circ \). **Navigation Options:** Use the 'Previous' button to revisit prior problems, or select any of the numbers from 1 to 12 to navigate to specific questions within the series. This will help in reviewing or skipping to different parts of the problem set according to necessity.
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