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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![### Understanding Circle Angles
#### Problem Statement:
- **Question:** What is \( m \angle TWU \)?
#### Diagram Explanation:
- This is a circle with center \( W \).
- Points \( V \), \( U \), and \( T \) lie on the circumference of the circle.
- Line segments \( VW \), \( UW \), and \( TW \) are radii of the circle, forming angles at the center.
- Angle \( VWU \) measures \( 120^\circ \).
- Angle \( VWT \) measures \( 150^\circ \).
- The task is to determine the measure of angle \( TWU \) (denoted as \( m \angle TWU \)).
#### Solution:
1. **Sum of Angles at Point \( W \):**
- The sum of angles around point \( W \) is \( 360^\circ \) since it is the center of the circle.
2. **Calculation:**
- \( m \angle VWU = 120^\circ \)
- \( m \angle VWT = 150^\circ \)
- \( m \angle TWU \) is therefore:
\[
m \angle TWU = 360^\circ - (120^\circ + 150^\circ) = 360^\circ - 270^\circ = 90^\circ
\]
#### Conclusion:
\[ m \angle TWU = 90^\circ \]
By completing this process, we find that the measure of \( \angle TWU \) is \( 90^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F718438f1-000a-489a-b339-ddbb88468aee%2Fe3f1c762-c423-41c1-8819-2c5a4efdb69a%2Fmi9jud8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Circle Angles
#### Problem Statement:
- **Question:** What is \( m \angle TWU \)?
#### Diagram Explanation:
- This is a circle with center \( W \).
- Points \( V \), \( U \), and \( T \) lie on the circumference of the circle.
- Line segments \( VW \), \( UW \), and \( TW \) are radii of the circle, forming angles at the center.
- Angle \( VWU \) measures \( 120^\circ \).
- Angle \( VWT \) measures \( 150^\circ \).
- The task is to determine the measure of angle \( TWU \) (denoted as \( m \angle TWU \)).
#### Solution:
1. **Sum of Angles at Point \( W \):**
- The sum of angles around point \( W \) is \( 360^\circ \) since it is the center of the circle.
2. **Calculation:**
- \( m \angle VWU = 120^\circ \)
- \( m \angle VWT = 150^\circ \)
- \( m \angle TWU \) is therefore:
\[
m \angle TWU = 360^\circ - (120^\circ + 150^\circ) = 360^\circ - 270^\circ = 90^\circ
\]
#### Conclusion:
\[ m \angle TWU = 90^\circ \]
By completing this process, we find that the measure of \( \angle TWU \) is \( 90^\circ \).
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