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
Concept explainers
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
Topic Video
Question
Transcribed Image Text:**Match the different arcs with the correct measurement.**
Below is a diagram of a circle with center labeled as G. The circle is divided into four segments by radii GD, GC, and GF, along with line GE. The segment arc DE at the top right of the circle is measured as 104°. The points on the circle perimeter are labeled as:
- C (left side of the circle)
- D (top point on the circle)
- E (right side of the circle)
- F (bottom of the circle)
### Detailed Explanation of the Diagram:
- The center of the circle is labeled as G.
- The line segments GD, GC, GE, and GF are the radii of the circle that meet at the center.
- The angle GDG is denoted with 104°, indicating the measure of arc DE.
The task is to determine and match the measurements of the other arcs labeled C, G, and F in relation to the given segments.
![**Educational Content on Angles and Measurements in Polygons**
Welcome to our section on understanding angles and measurements in polygons. Below is an interactive practice question that will help you to identify the correct angle measures for specific points in a polygon.
### Interactive Question
#### Given Diagrams and Measures
In the figure provided, you need to match the following angle measures to their respective points in the polygon.
###### Points and Angles:
1. \( \angle mDE \)
2. \( \angle mFE \)
3. \( \angle mDEF \)
4. \( \angle mCFD \)
5. \( \angle mDFE \)
On the right are dropdowns where you are supposed to select the correct angle measures for each respective point in the polygon. The available angle measures are as follows:
- **76°**
- **104°**
- **180°**
- **256°**
- **284°**
#### Matching Dropdowns
- For \( \angle mDE \):
- [Select the angle measure from the dropdown]
- For \( \angle mFE \):
- [Select the angle measure from the dropdown]
- For \( \angle mDEF \):
- [Select the angle measure from the dropdown]
- For \( \angle mCFD \):
- [Select the angle measure from the dropdown]
- For \( \angle mDFE \):
- [Select the angle measure from the dropdown]
#### Navigation
At the bottom of the problem window, you may find navigational buttons that allow you to move through different questions:
- **Previous Button:** Navigate to the previous question.
- **Pages 7 to 15:** Directly navigate to any specific question in this range.
- **Current Page Indicator:** Page 12 is highlighted, indicating that it is the current page you are working on.
### How to Solve:
1. Review the properties of the polygon provided.
2. Use your knowledge of internal and external angles to determine the correct measures.
3. Select the appropriate angle from the dropdown for each point listed.
Feel free to use geometrical principles and the sum of internal angles in polygons to assist in finding the solutions. Good luck!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32fdead-cf8a-44ab-a7f8-9f10e201d4c1%2F61fdd901-4dca-4279-87a0-a3c978491fa1%2Fx3k144_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content on Angles and Measurements in Polygons**
Welcome to our section on understanding angles and measurements in polygons. Below is an interactive practice question that will help you to identify the correct angle measures for specific points in a polygon.
### Interactive Question
#### Given Diagrams and Measures
In the figure provided, you need to match the following angle measures to their respective points in the polygon.
###### Points and Angles:
1. \( \angle mDE \)
2. \( \angle mFE \)
3. \( \angle mDEF \)
4. \( \angle mCFD \)
5. \( \angle mDFE \)
On the right are dropdowns where you are supposed to select the correct angle measures for each respective point in the polygon. The available angle measures are as follows:
- **76°**
- **104°**
- **180°**
- **256°**
- **284°**
#### Matching Dropdowns
- For \( \angle mDE \):
- [Select the angle measure from the dropdown]
- For \( \angle mFE \):
- [Select the angle measure from the dropdown]
- For \( \angle mDEF \):
- [Select the angle measure from the dropdown]
- For \( \angle mCFD \):
- [Select the angle measure from the dropdown]
- For \( \angle mDFE \):
- [Select the angle measure from the dropdown]
#### Navigation
At the bottom of the problem window, you may find navigational buttons that allow you to move through different questions:
- **Previous Button:** Navigate to the previous question.
- **Pages 7 to 15:** Directly navigate to any specific question in this range.
- **Current Page Indicator:** Page 12 is highlighted, indicating that it is the current page you are working on.
### How to Solve:
1. Review the properties of the polygon provided.
2. Use your knowledge of internal and external angles to determine the correct measures.
3. Select the appropriate angle from the dropdown for each point listed.
Feel free to use geometrical principles and the sum of internal angles in polygons to assist in finding the solutions. Good luck!
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