   Chapter 7.3, Problem 37E 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

Find the measure of a central angle of a regular polygon that has 54 diagonals.

To determine

To find:

The measure of a central angle of a regular polygon.

Explanation

Approach:

1) The number of diagonals of a regular polygon of n sides is given by D=n(n3)2

2) The measure of any central angle of a regular polygon of n sides is given by c=360n

Calculation:

It is given the regular polygon has 54 diagonals.

Use the formula for the number of diagonals of a regular polygon, D=n(n3)2

Substitute D = 54 in D=n(n3)2

54=n(n3)2n(n3)=108n23n=108n23n108=0n212n+9n

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