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Math
GeometryElementary Geometry for College Students6th Edition

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

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

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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(n−3)2

(2) The measure of each interior angle of a regular polygon of n sides is given by I=(n−2)⋅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(n−3)2 to calculate the number of diagonals.

D=8(8−3)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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Sect-2.1 P-1ESect-2.1 P-2ESect-2.1 P-3ESect-2.1 P-4ESect-2.1 P-5ESect-2.1 P-6ESect-2.1 P-7ESect-2.1 P-8ESect-2.1 P-9ESect-2.1 P-10E
Sect-2.1 P-11ESect-2.1 P-12ESect-2.1 P-13ESect-2.1 P-14ESect-2.1 P-15ESect-2.1 P-16ESect-2.1 P-17ESect-2.1 P-18ESect-2.1 P-19ESect-2.1 P-20ESect-2.1 P-21ESect-2.1 P-22ESect-2.1 P-23ESect-2.1 P-24ESect-2.1 P-25ESect-2.1 P-26ESect-2.1 P-27ESect-2.1 P-28ESect-2.1 P-29ESect-2.1 P-30ESect-2.1 P-31ESect-2.1 P-32ESect-2.1 P-33ESect-2.1 P-34ESect-2.1 P-35ESect-2.1 P-36ESect-2.2 P-1ESect-2.2 P-2ESect-2.2 P-3ESect-2.2 P-4ESect-2.2 P-5ESect-2.2 P-6ESect-2.2 P-7ESect-2.2 P-8ESect-2.2 P-9ESect-2.2 P-10ESect-2.2 P-11ESect-2.2 P-12ESect-2.2 P-13ESect-2.2 P-14ESect-2.2 P-15ESect-2.2 P-16ESect-2.2 P-17ESect-2.2 P-18ESect-2.2 P-19ESect-2.2 P-20ESect-2.2 P-21ESect-2.2 P-22ESect-2.2 P-23ESect-2.2 P-24ESect-2.2 P-25ESect-2.2 P-26ESect-2.2 P-27ESect-2.2 P-28ESect-2.2 P-29ESect-2.2 P-30ESect-2.2 P-31ESect-2.2 P-32ESect-2.2 P-33ESect-2.2 P-34ESect-2.3 P-1ESect-2.3 P-2ESect-2.3 P-3ESect-2.3 P-4ESect-2.3 P-5ESect-2.3 P-6ESect-2.3 P-7ESect-2.3 P-8ESect-2.3 P-9ESect-2.3 P-10ESect-2.3 P-11ESect-2.3 P-12ESect-2.3 P-13ESect-2.3 P-14ESect-2.3 P-15ESect-2.3 P-16ESect-2.3 P-17ESect-2.3 P-18ESect-2.3 P-19ESect-2.3 P-20ESect-2.3 P-21ESect-2.3 P-22ESect-2.3 P-23ESect-2.3 P-24ESect-2.3 P-25ESect-2.3 P-26ESect-2.3 P-27ESect-2.3 P-28ESect-2.3 P-29ESect-2.3 P-30ESect-2.3 P-31ESect-2.3 P-32ESect-2.3 P-33ESect-2.3 P-34ESect-2.3 P-35ESect-2.3 P-36ESect-2.3 P-37ESect-2.3 P-38ESect-2.4 P-1ESect-2.4 P-2ESect-2.4 P-3ESect-2.4 P-4ESect-2.4 P-5ESect-2.4 P-6ESect-2.4 P-7ESect-2.4 P-8ESect-2.4 P-9ESect-2.4 P-10ESect-2.4 P-11ESect-2.4 P-12ESect-2.4 P-13ESect-2.4 P-14ESect-2.4 P-15ESect-2.4 P-16ESect-2.4 P-17ESect-2.4 P-18ESect-2.4 P-19ESect-2.4 P-20ESect-2.4 P-21ESect-2.4 P-22ESect-2.4 P-23ESect-2.4 P-24ESect-2.4 P-25ESect-2.4 P-26ESect-2.4 P-27ESect-2.4 P-28ESect-2.4 P-29ESect-2.4 P-30ESect-2.4 P-31ESect-2.4 P-32ESect-2.4 P-33ESect-2.4 P-34ESect-2.4 P-35ESect-2.4 P-36ESect-2.4 P-37ESect-2.4 P-38ESect-2.4 P-39ESect-2.4 P-40ESect-2.4 P-41ESect-2.4 P-42ESect-2.4 P-43ESect-2.4 P-44ESect-2.4 P-45ESect-2.4 P-46ESect-2.4 P-47ESect-2.4 P-48ESect-2.4 P-49ESect-2.4 P-50ESect-2.5 P-1ESect-2.5 P-2ESect-2.5 P-3ESect-2.5 P-4ESect-2.5 P-5ESect-2.5 P-6ESect-2.5 P-7ESect-2.5 P-8ESect-2.5 P-9ESect-2.5 P-10ESect-2.5 P-11ESect-2.5 P-12ESect-2.5 P-13ESect-2.5 P-14ESect-2.5 P-15ESect-2.5 P-16ESect-2.5 P-17ESect-2.5 P-18ESect-2.5 P-19ESect-2.5 P-20ESect-2.5 P-21ESect-2.5 P-22ESect-2.5 P-23ESect-2.5 P-24ESect-2.5 P-25ESect-2.5 P-26ESect-2.5 P-27ESect-2.5 P-28ESect-2.5 P-29ESect-2.5 P-30ESect-2.5 P-31ESect-2.5 P-32ESect-2.5 P-33ESect-2.5 P-34ESect-2.5 P-35ESect-2.5 P-36ESect-2.5 P-37ESect-2.5 P-38ESect-2.5 P-39ESect-2.5 P-40ESect-2.5 P-41ESect-2.5 P-42ESect-2.5 P-43ESect-2.5 P-44ESect-2.5 P-45ESect-2.5 P-46ESect-2.5 P-47ESect-2.6 P-1ESect-2.6 P-2ESect-2.6 P-3ESect-2.6 P-4ESect-2.6 P-5ESect-2.6 P-6ESect-2.6 P-7ESect-2.6 P-8ESect-2.6 P-9ESect-2.6 P-10ESect-2.6 P-11ESect-2.6 P-12ESect-2.6 P-13ESect-2.6 P-14ESect-2.6 P-15ESect-2.6 P-16ESect-2.6 P-17ESect-2.6 P-18ESect-2.6 P-19ESect-2.6 P-20ESect-2.6 P-21ESect-2.6 P-22ESect-2.6 P-23ESect-2.6 P-24ESect-2.6 P-25ESect-2.6 P-26ESect-2.6 P-27ESect-2.6 P-28ESect-2.6 P-29ESect-2.6 P-30ESect-2.6 P-31ESect-2.6 P-32ESect-2.6 P-33ESect-2.6 P-34ESect-2.6 P-35ESect-2.6 P-36ESect-2.CR P-1CRSect-2.CR P-2CRSect-2.CR P-3CRSect-2.CR P-4CRSect-2.CR P-5CRSect-2.CR P-6CRSect-2.CR P-7CRSect-2.CR P-8CRSect-2.CR P-9CRSect-2.CR P-10CRSect-2.CR P-11CRSect-2.CR P-12CRSect-2.CR P-13CRSect-2.CR P-14CRSect-2.CR P-15CRSect-2.CR P-16CRSect-2.CR P-17CRSect-2.CR P-18CRSect-2.CR P-19CRSect-2.CR P-20CRSect-2.CR P-21CRSect-2.CR P-22CRSect-2.CR P-23CRSect-2.CR P-24CRSect-2.CR P-25CRSect-2.CR P-26CRSect-2.CR P-27CRSect-2.CR P-28CRSect-2.CR P-29CRSect-2.CR P-30CRSect-2.CR P-31CRSect-2.CR P-32CRSect-2.CR P-33CRSect-2.CR P-34CRSect-2.CR P-35CRSect-2.CR P-36CRSect-2.CR P-37CRSect-2.CR P-38CRSect-2.CR P-39CRSect-2.CR P-40CRSect-2.CR P-41CRSect-2.CR P-42CRSect-2.CR P-43CRSect-2.CR P-44CRSect-2.CR P-45CRSect-2.CR P-46CRSect-2.CR P-47CRSect-2.CT P-1CTSect-2.CT P-2CTSect-2.CT P-3CTSect-2.CT P-4CTSect-2.CT P-5CTSect-2.CT P-6CTSect-2.CT P-7CTSect-2.CT P-8CTSect-2.CT P-9CTSect-2.CT P-10CTSect-2.CT P-11CTSect-2.CT P-12CTSect-2.CT P-13CTSect-2.CT P-14CTSect-2.CT P-15CTSect-2.CT P-16CTSect-2.CT P-17CTSect-2.CT P-18CTSect-2.CT P-19CT

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