   Chapter 7.3, Problem 41E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

A regular polygon of n sides has an interior angle whose measure is 12 degrees smaller than the measure of the interior angle of the regular polygon with (n + 1) sides. Find n and name the type of polygon that has n sides.

To determine

To find:

The number of sides of a regular polygon and its type.

Explanation

Approach:

The measure of each interior angle of a regular polygon is given by I=(n2)180n

Calculation:

The measure of each interior angle of a regular polygon of sides n is given by I=(n2)180n

The measure of each interior angle of a regular polygon of sides n + 1 is given by I=(n1)180n+1

According to the question, (n1)180n+1(n2)180n=12

(n1)180n+1(n2)180n=12n1n+1n2n=115n(n1)x

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