Prove that an exterior angle of a regular polygon is equal to the angle at the center?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Prove that an exterior angle of a regular polygon is equal to the angle at the center?

 

Expert Solution
Step 1

Let us consider a regular n-polygon 

We know that the sum of the exterior angles of a polygon is = 360 degrees 

So, the sum of the n exterior angles of that polygon is = 360 degrees

1 exterior angle= 360/n degrees

 

 

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