Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Title: Calculating the Sum of Vertex Angles in a Concave Octagon**
**Description:**
To determine the sum of all the vertex angles in a concave octagon, use the formula for the sum of interior angles of a polygon. The formula is:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides.
For an octagon (\( n = 8 \)):
\[ \text{Sum of interior angles} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ \]
**Diagram:**
The provided diagram is a visual representation of a concave octagon. The design showcases eight sides, with one or more interior angles greater than 180 degrees, distinguishing it from a convex octagon.
**Conclusion:**
The sum of all the vertex angles in the concave octagon is:
\[ \boxed{1080^\circ} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11a562fb-23cb-468c-b02a-8a9b4a9af356%2F16ac619c-f91e-479a-b97e-6a41cc86c6a4%2F90hyl8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating the Sum of Vertex Angles in a Concave Octagon**
**Description:**
To determine the sum of all the vertex angles in a concave octagon, use the formula for the sum of interior angles of a polygon. The formula is:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides.
For an octagon (\( n = 8 \)):
\[ \text{Sum of interior angles} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ \]
**Diagram:**
The provided diagram is a visual representation of a concave octagon. The design showcases eight sides, with one or more interior angles greater than 180 degrees, distinguishing it from a convex octagon.
**Conclusion:**
The sum of all the vertex angles in the concave octagon is:
\[ \boxed{1080^\circ} \]
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