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
Related questions
Question
![**Problem: Sum of Interior Angles of a Polygon**
**Question:** Find the sum of the measures of the interior angles in the figure.
*Description:*
The question is accompanied by an image of a polygon. The polygon has five sides, making it a pentagon.
**Explanation:**
To find the sum of the interior angles of a 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 the given figure (a pentagon):
\[ n = 5 \]
\[ \text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ \]
Therefore, the sum of the measures of the interior angles in the given pentagon is \( 540^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4963a1b7-231e-4415-aa15-591e301cddd8%2F94d3c27f-65b8-43ca-a7e1-e8c2c1d09d77%2Fr7m3nw.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Sum of Interior Angles of a Polygon**
**Question:** Find the sum of the measures of the interior angles in the figure.
*Description:*
The question is accompanied by an image of a polygon. The polygon has five sides, making it a pentagon.
**Explanation:**
To find the sum of the interior angles of a 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 the given figure (a pentagon):
\[ n = 5 \]
\[ \text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ \]
Therefore, the sum of the measures of the interior angles in the given pentagon is \( 540^\circ \).
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