   Chapter 2.CR, Problem 25CR ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
3 views

# Complete the following table for regular polygons. Number of sides 8 12 20 Measure of each exterior ∠ 24 36 Measure of each interior ∠ 157.5 178 Number of diagonals

To determine

To Complete:

The given table.

Explanation

Given:

The following table for regular polygons’

 Number of sides 8 12 20 Measure of each exterior ∠ 24 36 Measure of each interior ∠ 157.5 178 Number of diagonals

Concept:

(1) The total number of diagonals D in a polygon of n sides is given by the formula D=n(n3)2

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

(3) The measure of each exterior angle of a regular polygon of n sides is given by E=360°n.

Calculation:

The complete table for regular polygon is shown as follows,

 Number of sides 8 12 20 15 10 16 180 Measure of each exterior ∠ 45 30 18 24 36 22.5 2 Measure of each interior ∠ 135 150 162 156 144 157.5 178 Number of diagonals 20 54 170 90 35 104 15930

Consider the regular polygon of 8 sides. That is, n=8.

Substitute 8 for n in D=n(n3)2 to calculate the number of diagonals.

D=8(83)2=4×5=20

So, the number of diagonals in regular polygon of 8 sides is 20.

Substitute 8 for n in E=360°n to calculate the measure of each exterior angle.

E=3608=45

So, the measure of each exterior angle of a regular polygon of 8 sides is 45.

Now, consider the polygon having measure of each exterior angle E=24.

Substitute 24 for E in E=360n to calculate the number of sides of the polygon

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