Find \( m\angle AUV \) if \( m\angle TUA = 31^\circ \) and \( m\angle TUV = 121^\circ \). **Diagram Explanation:** The image shows three points labeled A, U, and V, with two intersecting lines forming angles at point U. The angle \( \angle TUA \) is an angle between points T and A with U as the vertex. The angle \( \angle TUV \) is between points T and V with U as the vertex. The problem requests the calculation of \( m\angle AUV \). To solve: Using the angle addition postulate: \[ m\angle TUV = m\angle TUA + m\angle AUV \] Given: \[ m\angle TUV = 121^\circ \] \[ m\angle TUA = 31^\circ \] We solve for \( m\angle AUV \): \[ m\angle AUV = m\angle TUV - m\angle TUA \] \[ m\angle AUV = 121^\circ - 31^\circ \] \[ m\angle AUV = 90^\circ \] Thus, \( m\angle AUV = 90^\circ \).
Find \( m\angle AUV \) if \( m\angle TUA = 31^\circ \) and \( m\angle TUV = 121^\circ \). **Diagram Explanation:** The image shows three points labeled A, U, and V, with two intersecting lines forming angles at point U. The angle \( \angle TUA \) is an angle between points T and A with U as the vertex. The angle \( \angle TUV \) is between points T and V with U as the vertex. The problem requests the calculation of \( m\angle AUV \). To solve: Using the angle addition postulate: \[ m\angle TUV = m\angle TUA + m\angle AUV \] Given: \[ m\angle TUV = 121^\circ \] \[ m\angle TUA = 31^\circ \] We solve for \( m\angle AUV \): \[ m\angle AUV = m\angle TUV - m\angle TUA \] \[ m\angle AUV = 121^\circ - 31^\circ \] \[ m\angle AUV = 90^\circ \] Thus, \( m\angle AUV = 90^\circ \).
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
Related questions
Question
![Find \( m\angle AUV \) if \( m\angle TUA = 31^\circ \) and \( m\angle TUV = 121^\circ \).
**Diagram Explanation:**
The image shows three points labeled A, U, and V, with two intersecting lines forming angles at point U. The angle \( \angle TUA \) is an angle between points T and A with U as the vertex. The angle \( \angle TUV \) is between points T and V with U as the vertex. The problem requests the calculation of \( m\angle AUV \).
To solve:
Using the angle addition postulate:
\[ m\angle TUV = m\angle TUA + m\angle AUV \]
Given:
\[ m\angle TUV = 121^\circ \]
\[ m\angle TUA = 31^\circ \]
We solve for \( m\angle AUV \):
\[ m\angle AUV = m\angle TUV - m\angle TUA \]
\[ m\angle AUV = 121^\circ - 31^\circ \]
\[ m\angle AUV = 90^\circ \]
Thus, \( m\angle AUV = 90^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3da7d1a8-74f8-44b4-962a-fad662690b55%2F58d7d6e1-d0cc-4f3b-b5d8-17ce8a009acb%2Fzhk0zvd.jpeg&w=3840&q=75)
Transcribed Image Text:Find \( m\angle AUV \) if \( m\angle TUA = 31^\circ \) and \( m\angle TUV = 121^\circ \).
**Diagram Explanation:**
The image shows three points labeled A, U, and V, with two intersecting lines forming angles at point U. The angle \( \angle TUA \) is an angle between points T and A with U as the vertex. The angle \( \angle TUV \) is between points T and V with U as the vertex. The problem requests the calculation of \( m\angle AUV \).
To solve:
Using the angle addition postulate:
\[ m\angle TUV = m\angle TUA + m\angle AUV \]
Given:
\[ m\angle TUV = 121^\circ \]
\[ m\angle TUA = 31^\circ \]
We solve for \( m\angle AUV \):
\[ m\angle AUV = m\angle TUV - m\angle TUA \]
\[ m\angle AUV = 121^\circ - 31^\circ \]
\[ m\angle AUV = 90^\circ \]
Thus, \( m\angle AUV = 90^\circ \).
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