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1. Use the Polygon Angle-Sum Theorem to find the sum of INTERIOR angles of a polygon with 13 sides. Work: Sum: degrees

1. Use the Polygon Angle-Sum Theorem to find the sum of INTERIOR angles of a polygon with 13 sides. Work: Sum: degrees

Elementary Geometry For College Students, 7e
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.
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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