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What is mZTWU? V m4TWU = 120° 150⁰ W O T U

What is mZTWU? V m4TWU = 120° 150⁰ W O T U

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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### 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 \( 90^\circ \).
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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