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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![### Inscribed Angle in a Circle
#### Problem Statement
\(\angle XYZ\) is an inscribed angle in circle \(O\) with \(m \overset{\frown}{XZ} = 127^\circ\). Determine the \(m \angle XYZ\).
### Diagram Explanation
The diagram shows a circle with center \(O\). Points \(X\) and \(Z\) lie on the circumference of the circle, with an arc \(XZ\) created between them. There is an inscribed angle \(\angle XYZ\) where point \(Y\) is also on the circumference, creating the angle \(\angle XYZ\).
The measure of the arc \(XZ\) is given as \(127^\circ\).
### Multiple Choice Options:
A. \(63.5^\circ\)
B. \(53^\circ\)
C. \(26.5^\circ\)
D. \(127^\circ\)
### Solution:
To determine \(m \angle XYZ\), recall the property of inscribed angles:
- **An inscribed angle is half the measure of its intercepted arc.**
Given:
- \(m \overset{\frown}{XZ} = 127^\circ\)
Thus,
\[ m \angle XYZ = \frac{1}{2} \times m \overset{\frown}{XZ} \]
\[ m \angle XYZ = \frac{1}{2} \times 127^\circ \]
\[ m \angle XYZ = 63.5^\circ \]
So the correct answer is:
**A. \(63.5^\circ\)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa242a625-2826-4f00-ad8f-039422d3d327%2Fda4fa44e-51df-40b1-95c6-c4d9c38c68c7%2Fa8bdjb2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Inscribed Angle in a Circle
#### Problem Statement
\(\angle XYZ\) is an inscribed angle in circle \(O\) with \(m \overset{\frown}{XZ} = 127^\circ\). Determine the \(m \angle XYZ\).
### Diagram Explanation
The diagram shows a circle with center \(O\). Points \(X\) and \(Z\) lie on the circumference of the circle, with an arc \(XZ\) created between them. There is an inscribed angle \(\angle XYZ\) where point \(Y\) is also on the circumference, creating the angle \(\angle XYZ\).
The measure of the arc \(XZ\) is given as \(127^\circ\).
### Multiple Choice Options:
A. \(63.5^\circ\)
B. \(53^\circ\)
C. \(26.5^\circ\)
D. \(127^\circ\)
### Solution:
To determine \(m \angle XYZ\), recall the property of inscribed angles:
- **An inscribed angle is half the measure of its intercepted arc.**
Given:
- \(m \overset{\frown}{XZ} = 127^\circ\)
Thus,
\[ m \angle XYZ = \frac{1}{2} \times m \overset{\frown}{XZ} \]
\[ m \angle XYZ = \frac{1}{2} \times 127^\circ \]
\[ m \angle XYZ = 63.5^\circ \]
So the correct answer is:
**A. \(63.5^\circ\)**
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