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
![**Question 17: Determine \( m \angle S \) if \( m \angle V = 64^\circ \).**
**Diagram Description:**
The image contains a parallelogram labeled \( STUV \). The sides \( ST \) and \( UV \) are marked as equal, and the sides \( SV \) and \( TU \) are also marked as equal.
**Options:**
- A) \( m \angle S = 64^\circ \)
- B) \( m \angle S = 128^\circ \)
- C) \( m \angle S = 116^\circ \)
- D) \( m \angle S = 68^\circ \)
**Explanation:**
In a parallelogram, opposite angles are equal, and adjacent angles are supplementary. Given \( m \angle V = 64^\circ \), we need to find \( m \angle S \).
Because \( V \) and \( S \) are adjacent angles, they are supplementary:
\[ m \angle V + m \angle S = 180^\circ \]
\[ 64^\circ + m \angle S = 180^\circ \]
\[ m \angle S = 180^\circ - 64^\circ = 116^\circ \]
Thus, the correct answer is:
- C) \( m \angle S = 116^\circ \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbcee96d-8391-4179-ada6-2179ee125bd4%2F69d2cde1-2154-4772-b664-d36018ddc49d%2Fn6efctr_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 17: Determine \( m \angle S \) if \( m \angle V = 64^\circ \).**
**Diagram Description:**
The image contains a parallelogram labeled \( STUV \). The sides \( ST \) and \( UV \) are marked as equal, and the sides \( SV \) and \( TU \) are also marked as equal.
**Options:**
- A) \( m \angle S = 64^\circ \)
- B) \( m \angle S = 128^\circ \)
- C) \( m \angle S = 116^\circ \)
- D) \( m \angle S = 68^\circ \)
**Explanation:**
In a parallelogram, opposite angles are equal, and adjacent angles are supplementary. Given \( m \angle V = 64^\circ \), we need to find \( m \angle S \).
Because \( V \) and \( S \) are adjacent angles, they are supplementary:
\[ m \angle V + m \angle S = 180^\circ \]
\[ 64^\circ + m \angle S = 180^\circ \]
\[ m \angle S = 180^\circ - 64^\circ = 116^\circ \]
Thus, the correct answer is:
- C) \( m \angle S = 116^\circ \)
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