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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![**Title: Applying the Polygon Angle-Sum Theorem**
**Objective:**
Use the Polygon Angle-Sum Theorem to find the sum of the interior angles of a polygon with 13 sides.
**Instructions:**
1. **Problem Statement:**
Use the Polygon Angle-Sum Theorem to find the sum of the interior angles of a polygon with 13 sides.
2. **Explanation:**
The Polygon Angle-Sum Theorem states that the sum of the interior angles of a polygon is given by the formula:
\[
(n - 2) \times 180^{\circ}
\]
Where \( n \) is the number of sides of the polygon.
3. **Work:**
- Identify the number of sides: \( n = 13 \)
- Substitute \( n \) into the formula:
\[
\text{Sum of interior angles} = (13 - 2) \times 180^{\circ}
\]
\[
\text{Sum of interior angles} = 11 \times 180^{\circ}
\]
\[
\text{Sum of interior angles} = 1980^{\circ}
\]
4. **Conclusion:**
The sum of the interior angles of a polygon with 13 sides is 1980 degrees.
5. **Sum:**
\[
\text{Sum: } 1980 \text{ degrees}
\]
This exercise helps illustrate the application of the Polygon Angle-Sum Theorem and provides a clear step-by-step solution for determining the sum of interior angles of any polygon given the number of sides.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1af553b6-fe39-4557-b38a-c0ab1fffe725%2F24edcff1-2a60-4e0c-984b-81471a43ee67%2Ffq3r6o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Applying the Polygon Angle-Sum Theorem**
**Objective:**
Use the Polygon Angle-Sum Theorem to find the sum of the interior angles of a polygon with 13 sides.
**Instructions:**
1. **Problem Statement:**
Use the Polygon Angle-Sum Theorem to find the sum of the interior angles of a polygon with 13 sides.
2. **Explanation:**
The Polygon Angle-Sum Theorem states that the sum of the interior angles of a polygon is given by the formula:
\[
(n - 2) \times 180^{\circ}
\]
Where \( n \) is the number of sides of the polygon.
3. **Work:**
- Identify the number of sides: \( n = 13 \)
- Substitute \( n \) into the formula:
\[
\text{Sum of interior angles} = (13 - 2) \times 180^{\circ}
\]
\[
\text{Sum of interior angles} = 11 \times 180^{\circ}
\]
\[
\text{Sum of interior angles} = 1980^{\circ}
\]
4. **Conclusion:**
The sum of the interior angles of a polygon with 13 sides is 1980 degrees.
5. **Sum:**
\[
\text{Sum: } 1980 \text{ degrees}
\]
This exercise helps illustrate the application of the Polygon Angle-Sum Theorem and provides a clear step-by-step solution for determining the sum of interior angles of any polygon given the number of sides.
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