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 Statement:**
In a regular polygon, the measure of each interior angle is 162°. How many sides does the polygon have?
**Solution:**
To find the number of sides in a regular polygon given the measure of an interior angle, use the formula:
\[ \text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n} \]
Where \( n \) is the number of sides.
Given:
Interior Angle = 162°
Plug the given value into the formula:
\[ 162 = \frac{(n-2) \times 180}{n} \]
Solve for \( n \):
1. Multiply both sides by \( n \):
\[ 162n = (n-2) \times 180 \]
2. Expand the right side:
\[ 162n = 180n - 360 \]
3. Rearrange the terms:
\[ 180n - 162n = 360 \]
4. Simplify:
\[ 18n = 360 \]
5. Divide by 18:
\[ n = 20 \]
**Conclusion:**
The polygon has 20 sides.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c711c79-350e-448c-80fc-5638f7277d94%2F716bd09f-3b46-4ae0-b5ae-444f91cc0dcf%2Fytivptm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
In a regular polygon, the measure of each interior angle is 162°. How many sides does the polygon have?
**Solution:**
To find the number of sides in a regular polygon given the measure of an interior angle, use the formula:
\[ \text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n} \]
Where \( n \) is the number of sides.
Given:
Interior Angle = 162°
Plug the given value into the formula:
\[ 162 = \frac{(n-2) \times 180}{n} \]
Solve for \( n \):
1. Multiply both sides by \( n \):
\[ 162n = (n-2) \times 180 \]
2. Expand the right side:
\[ 162n = 180n - 360 \]
3. Rearrange the terms:
\[ 180n - 162n = 360 \]
4. Simplify:
\[ 18n = 360 \]
5. Divide by 18:
\[ n = 20 \]
**Conclusion:**
The polygon has 20 sides.
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