In circle N with the measure of arc MP= 98°, find mZMNP. M N Answer: m MNP = Submit Answer attempt i out of P Type here to search Ae

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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### Educational Content on Circle Geometry

#### Problem Statement:
In circle \( N \) with the measure of arc \( MP = 98^\circ \), find \( m \angle MNP \).

![circle diagram](image-url)

#### Diagram Explanation:
The diagram depicts a circle centered at point \( N \) with endpoints \( M \) and \( P \) on the circle's circumference forming an arc. The measure of the arc \( MP \) is given as \( 98^\circ \). The angle \( \angle MNP \) is the angle formed at the center of the circle by radii \( NM \) and \( NP \).

#### Solution:
To find the measure of \( \angle MNP \) in circle \( N \) given that the measure of arc \( MP \) is \( 98^\circ \):

1. **Understanding Central Angles:**
   - The central angle \( \angle MNP \) is the angle whose vertex is at the center of the circle and whose sides (radii) intercept the arc \( MP \).

2. **Arc and Central Angle Relationship:**
   - The measure of a central angle \( \angle MNP \) is equal to the measure of the intercepted arc \( MP \).

Thus, 
\[ m \angle MNP = 98^\circ \]

#### Answer:
\[ m \angle MNP = 98^\circ \]

Submit your answer in the input box provided to check your solution.

(Answer: \( m \angle MNP = \_\_\_\_ \))

[Submit Answer Button]

Note: Attempt 1 out of 3.
Transcribed Image Text:### Educational Content on Circle Geometry #### Problem Statement: In circle \( N \) with the measure of arc \( MP = 98^\circ \), find \( m \angle MNP \). ![circle diagram](image-url) #### Diagram Explanation: The diagram depicts a circle centered at point \( N \) with endpoints \( M \) and \( P \) on the circle's circumference forming an arc. The measure of the arc \( MP \) is given as \( 98^\circ \). The angle \( \angle MNP \) is the angle formed at the center of the circle by radii \( NM \) and \( NP \). #### Solution: To find the measure of \( \angle MNP \) in circle \( N \) given that the measure of arc \( MP \) is \( 98^\circ \): 1. **Understanding Central Angles:** - The central angle \( \angle MNP \) is the angle whose vertex is at the center of the circle and whose sides (radii) intercept the arc \( MP \). 2. **Arc and Central Angle Relationship:** - The measure of a central angle \( \angle MNP \) is equal to the measure of the intercepted arc \( MP \). Thus, \[ m \angle MNP = 98^\circ \] #### Answer: \[ m \angle MNP = 98^\circ \] Submit your answer in the input box provided to check your solution. (Answer: \( m \angle MNP = \_\_\_\_ \)) [Submit Answer Button] Note: Attempt 1 out of 3.
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