2520 degrees

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
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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
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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