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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Question
![**Understanding Arc Measures:**
In this task, we are given a circle with various points and angles. The points on the circle are labeled \( U \), \( V \), \( T \), \( S \), and \( W \). The circle features key angles and arcs that will help in solving for the measure of arc \( WS \).
1. **Diagram Description:**
- Point \( U \) is positioned such that \( \angle U \) is marked as 40°.
- Point \( T \) is on the circumference, and the angle inside the circle, \( \angle TVS \), is 75°.
- A right angle (90°) is formed at \( \angle UT \), signified by the small square.
- The arc formed by \( \angle TVU \) (the angle opposite to 75° within the circle) is what we need to solve for.
2. **Goal:**
- To determine the measure of the arc \( WS \).
3. **Geometrical Insights:**
- In a circle, the sum of the angles around a point equals 360°.
- Analyzing the diagram and utilizing the given angles helps us set up the appropriate equations.
4. **Calculation Steps:**
- Using the given angle measures and understanding properties such as supplementary angles and the angle sum property, solve for the measure of arc \( WS \).
**Transcription of the question and diagram:**
----------------------
**Question:**
What is \( m \overset{\frown}{WS} \)?
**Diagram Explanation:**
- The diagram shows a circle with points \( U, V, T, S, \) and \( W \).
- There is a right angle (90°) at \( \angle UT \).
- \( \angle U \) is given as 40°.
- \( \angle TVS \) is given as 75°.
- We need to find \( m \overset{\frown}{WS} \).
**Form to fill the answer:**
\[ m \overset{\frown}{WS} = \underline{\hspace{3cm}} \]
----------------------
Use the given information and relevant geometric principles to solve for the arc measure accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32fdead-cf8a-44ab-a7f8-9f10e201d4c1%2Fdef1ac53-eb1b-4b8c-8f75-b24d1d223f9f%2Fjw4prmi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Arc Measures:**
In this task, we are given a circle with various points and angles. The points on the circle are labeled \( U \), \( V \), \( T \), \( S \), and \( W \). The circle features key angles and arcs that will help in solving for the measure of arc \( WS \).
1. **Diagram Description:**
- Point \( U \) is positioned such that \( \angle U \) is marked as 40°.
- Point \( T \) is on the circumference, and the angle inside the circle, \( \angle TVS \), is 75°.
- A right angle (90°) is formed at \( \angle UT \), signified by the small square.
- The arc formed by \( \angle TVU \) (the angle opposite to 75° within the circle) is what we need to solve for.
2. **Goal:**
- To determine the measure of the arc \( WS \).
3. **Geometrical Insights:**
- In a circle, the sum of the angles around a point equals 360°.
- Analyzing the diagram and utilizing the given angles helps us set up the appropriate equations.
4. **Calculation Steps:**
- Using the given angle measures and understanding properties such as supplementary angles and the angle sum property, solve for the measure of arc \( WS \).
**Transcription of the question and diagram:**
----------------------
**Question:**
What is \( m \overset{\frown}{WS} \)?
**Diagram Explanation:**
- The diagram shows a circle with points \( U, V, T, S, \) and \( W \).
- There is a right angle (90°) at \( \angle UT \).
- \( \angle U \) is given as 40°.
- \( \angle TVS \) is given as 75°.
- We need to find \( m \overset{\frown}{WS} \).
**Form to fill the answer:**
\[ m \overset{\frown}{WS} = \underline{\hspace{3cm}} \]
----------------------
Use the given information and relevant geometric principles to solve for the arc measure accurately.
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