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
![**Title: Calculating the Measure of an Angle in a Circle**
**Problem Statement:**
What is the measure of ∠YZV in the circle below?
**Diagram Description:**
The diagram consists of a circle with center Z and four radii creating four segments. The segments divide the circle into four sectors, labeled as follows:
- Sector XZY with angle 85°
- Sector UZV with angle 108°
- The other two sectors are not labeled with specific angles but are defined by points on the circle: V and W.
**Question:**
Find the measure of angle ∠YZV.
**Solution Steps:**
1. The sum of all angles around point Z should be 360°, as they form a complete circle.
2. Given:
- m∠XZY = 85°
- m∠UZV = 108°
3. Since the only angles given are ∠XZY and ∠UZV, the remaining two angles (including ∠YZV) must sum to the remaining degrees out of 360°.
4. Calculate m∠YZV:
\[
m∠YZV = 360° - (85° + 108°)
= 360° - 193°
= 167°
\]
**Answer:**
m∠YZV = 167° degrees
**Conclusion:**
By understanding the properties of angles around a point and using basic arithmetic, we found m∠YZV to be 167°.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43d2448d-3e96-4e40-abdb-281cc47928a3%2Fd1bb32b3-9be5-43ad-b035-6fc0a9b2d024%2Fo58wf0d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating the Measure of an Angle in a Circle**
**Problem Statement:**
What is the measure of ∠YZV in the circle below?
**Diagram Description:**
The diagram consists of a circle with center Z and four radii creating four segments. The segments divide the circle into four sectors, labeled as follows:
- Sector XZY with angle 85°
- Sector UZV with angle 108°
- The other two sectors are not labeled with specific angles but are defined by points on the circle: V and W.
**Question:**
Find the measure of angle ∠YZV.
**Solution Steps:**
1. The sum of all angles around point Z should be 360°, as they form a complete circle.
2. Given:
- m∠XZY = 85°
- m∠UZV = 108°
3. Since the only angles given are ∠XZY and ∠UZV, the remaining two angles (including ∠YZV) must sum to the remaining degrees out of 360°.
4. Calculate m∠YZV:
\[
m∠YZV = 360° - (85° + 108°)
= 360° - 193°
= 167°
\]
**Answer:**
m∠YZV = 167° degrees
**Conclusion:**
By understanding the properties of angles around a point and using basic arithmetic, we found m∠YZV to be 167°.
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