   Chapter 7.3, Problem 40E 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 exterior angle whose measure is 12 degrees larger than the measure of the exterior 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 exterior angle of a regular polygon is given by E=360n

Calculation:

The measure of each exterior angle of a regular polygon of sides n is given by E=360n

The measure of each exterior angle of a regular polygon of sides n + 1 is given by E=360n+1

According to the question, 360n360n+1=12

360n360n+1=1230n30n+1=11n1n+1=130n+1<

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