The sum of the interior angles of two regular polygons is 2520°. If the number of sides of one of the polygons is 3 less than twice the number of sides of the other, find the number of sides of each of the polygons.
The sum of the interior angles of two regular polygons is 2520°. If the number of sides of one of the polygons is 3 less than twice the number of sides of the other, find the number of sides of each of the polygons.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Problem Statement:**
The sum of the interior angles of two regular polygons is 2520°. If the number of sides of one of the polygons is 3 less than twice the number of sides of the other, find the number of sides of each of the polygons.
To solve this problem, consider the two polygons: let the number of sides of the first polygon be \( n \) and the number of sides of the second polygon be \( m \).
Given:
1. The sum of the interior angles of the two polygons is 2520°.
2. The number of sides of one polygon is 3 less than twice the number of sides of the other.
We know that the sum of the interior angles \( S \) of a polygon with \( k \) sides is given by the formula:
\[ S = (k - 2) \times 180° \]
Applying this formula to both polygons, we get:
\[ S_1 = (n - 2) \times 180° \]
\[ S_2 = (m - 2) \times 180° \]
From the first condition:
\[ (n - 2) \times 180° + (m - 2) \times 180° = 2520° \]
From the second condition:
\[ n = 2m - 3 \]
By substituting the second condition into the equation obtained from the first condition, we can solve for the number of sides \( n \) and \( m \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0436118d-47b7-4fa9-abd3-dac72bbeccd1%2Fddd6eb7f-13b9-46ba-aca5-de6915d43c0e%2Foy7qrb1q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The sum of the interior angles of two regular polygons is 2520°. If the number of sides of one of the polygons is 3 less than twice the number of sides of the other, find the number of sides of each of the polygons.
To solve this problem, consider the two polygons: let the number of sides of the first polygon be \( n \) and the number of sides of the second polygon be \( m \).
Given:
1. The sum of the interior angles of the two polygons is 2520°.
2. The number of sides of one polygon is 3 less than twice the number of sides of the other.
We know that the sum of the interior angles \( S \) of a polygon with \( k \) sides is given by the formula:
\[ S = (k - 2) \times 180° \]
Applying this formula to both polygons, we get:
\[ S_1 = (n - 2) \times 180° \]
\[ S_2 = (m - 2) \times 180° \]
From the first condition:
\[ (n - 2) \times 180° + (m - 2) \times 180° = 2520° \]
From the second condition:
\[ n = 2m - 3 \]
By substituting the second condition into the equation obtained from the first condition, we can solve for the number of sides \( n \) and \( m \).
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