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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![### Geometry: Sum of Interior Angles of a Polygon
#### Example Question:
*Find the sum of the measures of the interior angles of a convex 16-gon.*
#### Multiple-choice Options:
- ⭕ 180 degrees
- ⭕ 360 degrees
- ⭕ 2520 degrees
- ⭕ 2880 degrees
#### Explanation:
To find the sum of the interior angles of a convex polygon, you can use the formula:
\[ \text{Sum of Interior Angles} = (n - 2) \times 180^\circ \]
Where \( n \) is the number of sides in the polygon. For a 16-gon (16-sided polygon):
\[ \text{Sum of Interior Angles} = (16 - 2) \times 180^\circ \]
\[ \text{Sum of Interior Angles} = 14 \times 180^\circ \]
\[ \text{Sum of Interior Angles} = 2520^\circ \]
Thus, the correct answer is:
- ⭕ 2520 degrees](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47897a37-2eac-43d5-a731-3aff060a1d87%2F0267034d-b6f6-45dd-aaa2-f65204cb03b8%2Ffdy26n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry: Sum of Interior Angles of a Polygon
#### Example Question:
*Find the sum of the measures of the interior angles of a convex 16-gon.*
#### Multiple-choice Options:
- ⭕ 180 degrees
- ⭕ 360 degrees
- ⭕ 2520 degrees
- ⭕ 2880 degrees
#### Explanation:
To find the sum of the interior angles of a convex polygon, you can use the formula:
\[ \text{Sum of Interior Angles} = (n - 2) \times 180^\circ \]
Where \( n \) is the number of sides in the polygon. For a 16-gon (16-sided polygon):
\[ \text{Sum of Interior Angles} = (16 - 2) \times 180^\circ \]
\[ \text{Sum of Interior Angles} = 14 \times 180^\circ \]
\[ \text{Sum of Interior Angles} = 2520^\circ \]
Thus, the correct answer is:
- ⭕ 2520 degrees
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