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

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

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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### Finding the Measure of Arc NQ **Problem Statement:** Given the circle diagram with points M, N, R, P, Q, and the center O, where MQ and NR are diameters, find the measure of arc NQ. **Diagram Explanation:** In the circle: - Points M, N, R, P, and Q are on the circumference. - MQ and NR are diameters, meaning they pass through the center O and divide the circle into two equal halves. - Angle MON is given as 82 degrees. - Angle NOR is given as 63 degrees. ### Calculation: To find the measure of arc NQ, follow these steps: 1. **Calculate Central Angle of Remaining Arc:** Since MQ and NR are diameters, the sum of all angles around O is 360 degrees. Given: - Angle MON = 82 degrees - Angle NOR = 63 degrees The remaining central angle PRO: \[ \text{Angle PRO} = 360^\circ - 82^\circ - 63^\circ = 215^\circ \] 2. **Determine the Measure of Arc NQ:** The arc NQ corresponds to the central angle NOR which is across points N and Q. So, the measure of arc NQ is equal to the measure of central angle NOR, which is: \[ \text{Arc NQ} = 63^\circ \] **Answer:** The measure of arc NQ is \( 63^\circ \). **Interactive Question:** You may fill in the measure of arc NQ below for verification. **Input Box:** ```plaintext arc NQ: 63° ``` Once the value is entered, you may click "OK" to check your answer.
Transcribed Image Text:### Finding the Measure of Arc NQ **Problem Statement:** Given the circle diagram with points M, N, R, P, Q, and the center O, where MQ and NR are diameters, find the measure of arc NQ. **Diagram Explanation:** In the circle: - Points M, N, R, P, and Q are on the circumference. - MQ and NR are diameters, meaning they pass through the center O and divide the circle into two equal halves. - Angle MON is given as 82 degrees. - Angle NOR is given as 63 degrees. ### Calculation: To find the measure of arc NQ, follow these steps: 1. **Calculate Central Angle of Remaining Arc:** Since MQ and NR are diameters, the sum of all angles around O is 360 degrees. Given: - Angle MON = 82 degrees - Angle NOR = 63 degrees The remaining central angle PRO: \[ \text{Angle PRO} = 360^\circ - 82^\circ - 63^\circ = 215^\circ \] 2. **Determine the Measure of Arc NQ:** The arc NQ corresponds to the central angle NOR which is across points N and Q. So, the measure of arc NQ is equal to the measure of central angle NOR, which is: \[ \text{Arc NQ} = 63^\circ \] **Answer:** The measure of arc NQ is \( 63^\circ \). **Interactive Question:** You may fill in the measure of arc NQ below for verification. **Input Box:** ```plaintext arc NQ: 63° ``` Once the value is entered, you may click "OK" to check your answer.
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